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Ohio OST Geometry study materials
Ohio OST Geometry study resources

Ohio OST Geometry practice questions

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Question 1Geometry (Ohio's Learning Standards for Mathematics)

A quadrilateral has four right angles. Which additional single condition guarantees the quadrilateral is a square?

  1. The diagonals bisect each other.
  2. The diagonals are congruent.
  3. One pair of opposite sides is parallel.
  4. Two adjacent sides are congruent. Correct answer.

Explanation

A quadrilateral with four right angles is already a rectangle, so opposite sides are automatically parallel and the diagonals are automatically congruent and bisect each other. Adding that two adjacent sides are congruent forces all four sides to be congruent, which turns the rectangle into a square. The other three conditions are already true in every rectangle and add no new information.

Question 2Geometry (Ohio's Learning Standards for Mathematics)

Triangle ABC is similar to triangle DEF with a scale factor of 3 from ABC to DEF. If the area of triangle ABC is 10 square centimeters, what is the area of triangle DEF?

  1. 60 square centimeters
  2. 90 square centimeters Correct answer.
  3. 30 square centimeters
  4. 100 square centimeters

Explanation

For similar figures, the ratio of areas equals the square of the linear scale factor. Here the linear scale factor is 3, so the area ratio is 3 squared, which is 9. Multiplying 10 square centimeters by 9 gives 90 square centimeters.

Question 3Geometry (Ohio's Learning Standards for Mathematics)

In a circle with center O, a central angle measures 72 degrees. What is the measure of the inscribed angle that intercepts the same arc?

  1. 36 degrees Correct answer.
  2. 18 degrees
  3. 144 degrees
  4. 72 degrees

Explanation

An inscribed angle measures half the central angle that intercepts the same arc. Since the central angle is 72 degrees, the inscribed angle is 72 divided by 2, which is 36 degrees. This is the Inscribed Angle Theorem.

Question 4Geometry (Ohio's Learning Standards for Mathematics)

A right triangle has legs of length 5 and 12. What is the length of the hypotenuse?

  1. 60
  2. 13 Correct answer.
  3. 17
  4. 7

Explanation

By the Pythagorean Theorem, the hypotenuse squared equals the sum of the squares of the legs. Here 5 squared plus 12 squared equals 25 plus 144, which is 169, and the square root of 169 is 13. The triple 5-12-13 is a common Pythagorean triple.

Question 5Geometry (Ohio's Learning Standards for Mathematics)

A line segment has endpoints at (2, 3) and (8, 11). What are the coordinates of its midpoint?

  1. (6, 8)
  2. (10, 14)
  3. (3, 4)
  4. (5, 7) Correct answer.

Explanation

The midpoint formula averages the x-coordinates and the y-coordinates separately. The x-coordinate is (2 plus 8) divided by 2, which is 5, and the y-coordinate is (3 plus 11) divided by 2, which is 7. So the midpoint is (5, 7).

Question 6Geometry (Ohio's Learning Standards for Mathematics)

A cone has a radius of 3 centimeters and a height of 8 centimeters. Which expression gives its volume in cubic centimeters?

  1. 8 pi
  2. 24 pi Correct answer.
  3. 12 pi
  4. 72 pi

Explanation

The volume of a cone is one third times pi times the radius squared times the height. Here the radius squared is 9 and the height is 8, so the product is 72, and one third of 72 is 24. The volume is therefore 24 pi cubic centimeters.

Question 7Geometry (Ohio's Learning Standards for Mathematics)

A regular polygon has an interior angle measuring 135 degrees. How many sides does the polygon have?

  1. 8 Correct answer.
  2. 12
  3. 10
  4. 6

Explanation

Each interior angle of a regular polygon with n sides measures (n minus 2) times 180 divided by n degrees. Setting this equal to 135 gives 180n minus 360 equals 135n, so 45n equals 360 and n equals 8. The polygon is a regular octagon.

Question 8Geometry (Ohio's Learning Standards for Mathematics)

A transformation maps every point (x, y) to (x plus 4, y minus 2). Which single transformation is this?

  1. A dilation by a factor of 2 about the origin
  2. A rotation of 90 degrees about the origin
  3. A reflection across the line y equals x
  4. A translation 4 units right and 2 units down Correct answer.

Explanation

Adding to the x-coordinate shifts points horizontally and adding to the y-coordinate shifts them vertically. Here x increases by 4 and y decreases by 2, which is a translation 4 units right and 2 units down. Translations preserve size, shape, and orientation, consistent with this rule.

Question 9Geometry (Ohio's Learning Standards for Mathematics)

In a coordinate proof, points A(0, 0) and B(6, 0) are given. Point C is placed at (3, 4). Which statement about triangle ABC is true?

  1. It is right because AB is perpendicular to BC.
  2. It is isosceles because AC equals BC. Correct answer.
  3. It is scalene because all three side lengths differ.
  4. It is equilateral because all sides are equal.

Explanation

Using the distance formula, AC equals the square root of (3 squared plus 4 squared), which is 5, and BC equals the square root of (3 squared plus 4 squared), which is also 5. Since two sides are congruent, the triangle is isosceles. Side AB has length 6, so the triangle is not equilateral.

Question 10Geometry (Ohio's Learning Standards for Mathematics)

Two parallel lines are cut by a transversal. One interior angle on the left side of the transversal measures 65 degrees. What is the measure of its alternate interior angle on the opposite side of the transversal?

  1. 65 degrees Correct answer.
  2. 115 degrees
  3. 130 degrees
  4. 25 degrees

Explanation

When two parallel lines are cut by a transversal, alternate interior angles are congruent. The alternate interior angle lies on the opposite side of the transversal and between the parallel lines, so it has the same measure. Therefore it measures 65 degrees.

Question 11Geometry (Ohio's Learning Standards for Mathematics)

A circle has a radius of 6 centimeters and a central angle of 120 degrees. What is the arc length intercepted by the angle, in centimeters?

  1. 6 pi
  2. 4 pi Correct answer.
  3. 12 pi
  4. 2 pi

Explanation

Arc length equals the fraction of the circle times the circumference. The fraction is 120 divided by 360, which is one third, and the circumference is 2 pi times 6, which is 12 pi. One third of 12 pi is 4 pi centimeters.

Question 12Geometry (Ohio's Learning Standards for Mathematics)

A right circular cylinder has a radius of 4 inches and a height of 9 inches. What is its total surface area in square inches?

  1. 72 pi
  2. 144 pi
  3. 104 pi Correct answer.
  4. 88 pi

Explanation

Total surface area of a cylinder equals 2 pi r squared plus 2 pi r h. The two bases contribute 2 pi times 16, which is 32 pi, and the lateral surface contributes 2 pi times 4 times 9, which is 72 pi. Adding gives 104 pi square inches.

Question 13Geometry (Ohio's Learning Standards for Mathematics)

A dilation centered at the origin maps point P(4, 6) to P prime(10, 15). What is the scale factor of the dilation?

  1. 2.5 Correct answer.
  2. 1.5
  3. 0.4
  4. 6

Explanation

A dilation centered at the origin multiplies both coordinates by the same scale factor k. Dividing 10 by 4 gives 2.5, and dividing 15 by 6 also gives 2.5, so the scale factor is consistent. The scale factor is therefore 2.5.

Question 14Geometry (Ohio's Learning Standards for Mathematics)

A triangle has vertices A(1, 2), B(4, 2), and C(1, 6). The triangle is reflected across the x-axis. What are the coordinates of the image of C?

  1. (1, 6)
  2. (-1, -6)
  3. (-1, 6)
  4. (1, -6) Correct answer.

Explanation

Reflection across the x-axis keeps the x-coordinate and changes the sign of the y-coordinate, mapping (x, y) to (x, negative y). Applying this to C(1, 6) gives (1, negative 6). The x-coordinate stays 1.

Question 15Geometry (Ohio's Learning Standards for Mathematics)

In circle O, two chords intersect inside the circle. The segments of one chord have lengths 6 and 8. One segment of the other chord has length 4. What is the length of the other segment of that chord?

  1. 10
  2. 12 Correct answer.
  3. 48
  4. 3

Explanation

When two chords intersect inside a circle, the products of the segment lengths on each chord are equal. The first chord gives 6 times 8, which is 48, so the second chord must satisfy 4 times x equals 48. Solving gives x equals 12.

Question 16Geometry (Ohio's Learning Standards for Mathematics)

A tangent segment from an external point to a circle has length 9. A secant from the same point passes through the circle and has an external part of length 3. What is the length of the entire secant?

  1. 6
  2. 27 Correct answer.
  3. 9
  4. 12

Explanation

The tangent-secant theorem states that the tangent length squared equals the product of the external secant segment and the whole secant. So 9 squared, which is 81, equals 3 times the whole secant length. Dividing 81 by 3 gives 27.

Question 17Geometry (Ohio's Learning Standards for Mathematics)

A sector of a circle has a radius of 10 centimeters and a central angle of 90 degrees. What is the area of the sector in square centimeters?

  1. 25 pi Correct answer.
  2. 50 pi
  3. 10 pi
  4. 100 pi

Explanation

The area of a sector equals the fraction of the circle's area determined by the central angle. The circle's area is pi times 10 squared, which is 100 pi, and 90 divided by 360 is one fourth. One fourth of 100 pi is 25 pi square centimeters.

Question 18Geometry (Ohio's Learning Standards for Mathematics)

A rectangular prism has dimensions 3, 4, and 12. What is the length of its space diagonal?

  1. 169
  2. 13 Correct answer.
  3. 7
  4. 19

Explanation

The space diagonal of a rectangular prism equals the square root of the sum of the squares of its three dimensions. Here 3 squared plus 4 squared plus 12 squared equals 9 plus 16 plus 144, which is 169. The square root of 169 is 13.

Question 19Geometry (Ohio's Learning Standards for Mathematics)

A line passes through points (2, 5) and (6, 13). What is the equation of the line perpendicular to this line and passing through (4, 3)?

  1. y minus 3 equals negative 2 times (x minus 4)
  2. y minus 3 equals 2 times (x minus 4)
  3. y minus 3 equals one half times (x minus 4)
  4. y minus 3 equals negative one half times (x minus 4) Correct answer.

Explanation

The slope of the given line is (13 minus 5) divided by (6 minus 2), which is 8 divided by 4, or 2. Perpendicular lines have slopes that are negative reciprocals, so the perpendicular slope is negative one half. Using point-slope form through (4, 3) gives y minus 3 equals negative one half times (x minus 4).

Question 20Geometry (Ohio's Learning Standards for Mathematics)

A triangle has sides of length 7, 24, and 25. Which classification is correct?

  1. Right, because 7 squared plus 24 squared equals 25 squared. Correct answer.
  2. Acute, because the longest side squared is less than the sum of the squares of the other two.
  3. Equilateral, because all sides have integer lengths.
  4. Obtuse, because the longest side squared is greater than the sum of the squares of the other two.

Explanation

Compute 7 squared plus 24 squared, which is 49 plus 576, or 625, and note that 25 squared is also 625. Since the squares satisfy the Pythagorean relationship, the triangle is right. The converse of the Pythagorean Theorem confirms the angle opposite the 25 side is a right angle.

Question 21Geometry (Ohio's Learning Standards for Mathematics)

A regular hexagon is inscribed in a circle of radius 8. What is the area of the hexagon in square units?

  1. 48 square root of 3
  2. 64 square root of 3
  3. 192 square root of 3
  4. 96 square root of 3 Correct answer.

Explanation

A regular hexagon inscribed in a circle of radius r has side length r, so each side is 8. The hexagon divides into six equilateral triangles with side 8, each having area (square root of 3 divided by 4) times 64, which is 16 square root of 3. Multiplying by 6 gives 96 square root of 3.

Question 22Geometry (Ohio's Learning Standards for Mathematics)

In a circle, an angle formed by two secants intersecting outside the circle intercepts arcs measuring 100 degrees and 40 degrees. What is the measure of the angle?

  1. 70 degrees
  2. 30 degrees Correct answer.
  3. 140 degrees
  4. 60 degrees

Explanation

For an angle formed by two secants meeting outside a circle, the angle measure equals half the difference of the intercepted arcs. The difference is 100 minus 40, which is 60, and half of 60 is 30 degrees. The angle is therefore 30 degrees.

Question 23Geometry (Ohio's Learning Standards for Mathematics)

A cone and a cylinder have the same base radius and the same height. The cone is filled with water and poured into the empty cylinder. What fraction of the cylinder is filled?

  1. Two thirds
  2. One half
  3. One sixth
  4. One third Correct answer.

Explanation

A cone's volume is one third of the volume of a cylinder with the same base radius and height, because the cone formula includes a factor of one third. Pouring the full cone into the cylinder therefore fills exactly one third of the cylinder. This relationship holds for any matching radius and height.

Question 24Geometry (Ohio's Learning Standards for Mathematics)

Quadrilateral ABCD has vertices A(0, 0), B(4, 0), C(5, 3), and D(1, 3). Which statement correctly identifies the figure?

  1. It is a parallelogram but not a rhombus because adjacent sides are not congruent. Correct answer.
  2. It is a rhombus but not a parallelogram.
  3. It is a trapezoid because only one pair of sides is parallel.
  4. It is a rectangle because the diagonals are congruent.

Explanation

Sides AB and DC both have slope 0, and sides AD and BC both have slope 3, so both pairs of opposite sides are parallel and the figure is a parallelogram. Side AB has length 4 while side BC has length the square root of 10, so adjacent sides are not congruent and the figure is not a rhombus. The diagonals have different lengths, so it is not a rectangle either.

Question 25Geometry (Ohio's Learning Standards for Mathematics)

A right triangle has a hypotenuse of length 13 and one acute angle measuring 30 degrees. What is the length of the side opposite the 30 degree angle?

  1. 13 square root of 3
  2. 26
  3. 13 divided by the square root of 3
  4. 6.5 Correct answer.

Explanation

In a 30-60-90 triangle, the side opposite the 30 degree angle is half the hypotenuse. Since the hypotenuse is 13, that side is 13 divided by 2, which is 6.5. The side opposite the 60 degree angle would be 6.5 times the square root of 3.

Question 26Geometry (Ohio's Learning Standards for Mathematics)

A quadrilateral has four sides. Which additional condition guarantees that the quadrilateral is a parallelogram?

  1. One pair of opposite sides is both parallel and congruent
  2. The diagonals are perpendicular to each other
  3. Two consecutive angles are supplementary
  4. Both pairs of opposite angles are congruent Correct answer.

Explanation

A quadrilateral is a parallelogram exactly when both pairs of opposite angles are congruent, since congruence of opposite angles forces both pairs of opposite sides to be parallel. The other conditions either describe special parallelograms or fail to force both pairs of sides to be parallel.

Question 27Geometry (Ohio's Learning Standards for Mathematics)

A triangle has side lengths 9, 12, and 15. What is the area of the triangle in square units?

  1. 54 Correct answer.
  2. 90
  3. 72
  4. 108

Explanation

Because 9 squared plus 12 squared equals 15 squared, the triangle is right with legs 9 and 12. Its area is one half times 9 times 12, which equals 54 square units.

Question 28Geometry (Ohio's Learning Standards for Mathematics)

A circle is centered at the origin with radius 5. A line is tangent to the circle at the point (3, 4). What is the slope of this tangent line?

  1. negative four thirds
  2. three fourths
  3. four thirds
  4. negative three fourths Correct answer.

Explanation

The radius drawn to the point of tangency has slope 4/3, so the tangent line is perpendicular to it and has slope negative three fourths. Perpendicular slopes are negative reciprocals.

Question 29Geometry (Ohio's Learning Standards for Mathematics)

Two similar right triangles are compared. The smaller triangle has legs 6 and 8. The larger triangle has a hypotenuse of 25. What is the area of the larger triangle in square units?

  1. 75
  2. 120
  3. 150 Correct answer.
  4. 300

Explanation

The smaller triangle has hypotenuse 10, so the similarity ratio is 25 to 10, or 2.5. The larger legs are 15 and 20, giving area one half times 15 times 20, which is 150.

Question 30Geometry (Ohio's Learning Standards for Mathematics)

A point is chosen on a circle of radius 10 such that a chord through it has length 16. What is the distance from the center of the circle to this chord?

  1. 8
  2. 5
  3. 6 Correct answer.
  4. 4

Explanation

The perpendicular from the center to a chord bisects it, creating a right triangle with hypotenuse 10 and one leg 8. The distance is the other leg, which is 6 by the Pythagorean theorem.

Question 31Geometry (Ohio's Learning Standards for Mathematics)

A regular octagon is inscribed in a circle. What is the measure in degrees of each central angle formed by consecutive vertices?

  1. 60
  2. 45 Correct answer.
  3. 135
  4. 72

Explanation

A regular octagon divides the circle into eight congruent central angles. Dividing 360 degrees by 8 gives 45 degrees.

Question 32Geometry (Ohio's Learning Standards for Mathematics)

A sphere has a radius of 6 centimeters. What is its volume in cubic centimeters, expressed in terms of pi?

  1. 288 pi Correct answer.
  2. 216 pi
  3. 144 pi
  4. 864 pi

Explanation

The volume of a sphere is four thirds times pi times the cube of the radius. Substituting 6 gives four thirds times 216, which equals 288, so the volume is 288 pi cubic centimeters.

Question 33Geometry (Ohio's Learning Standards for Mathematics)

In a right triangle, the side adjacent to an acute angle measures 9 and the hypotenuse measures 15. Which expression gives the measure of the angle?

  1. inverse cosine of fifteen ninths
  2. inverse sine of nine fifteenths
  3. inverse cosine of nine fifteenths Correct answer.
  4. inverse tangent of nine fifteenths

Explanation

The cosine ratio relates the adjacent side to the hypotenuse, so cosine of the angle equals 9/15. To find the angle, take the inverse cosine of nine fifteenths.

Question 34Geometry (Ohio's Learning Standards for Mathematics)

A line segment has endpoints at (2, 1) and (8, 5). What are the coordinates of its midpoint?

  1. (3, 2)
  2. (5, 3) Correct answer.
  3. (6, 4)
  4. (10, 6)

Explanation

The midpoint formula averages the x-coordinates and the y-coordinates separately. Averaging 2 and 8 gives 5, and averaging 1 and 5 gives 3, so the midpoint is (5, 3).

Question 35Geometry (Ohio's Learning Standards for Mathematics)

A circle has equation x squared plus y squared minus 6x plus 4y minus 12 equals 0. What is the radius of the circle?

  1. 5 Correct answer.
  2. 25
  3. 12
  4. 4

Explanation

Completing the square gives (x minus 3) squared plus (y plus 2) squared equals 25. The right side is the square of the radius, so the radius is 5.

Question 36Geometry (Ohio's Learning Standards for Mathematics)

A transformation maps every point (x, y) to (negative y, x). Which single transformation is this?

  1. A reflection across the y-axis
  2. A rotation of 90 degrees counterclockwise about the origin Correct answer.
  3. A rotation of 180 degrees about the origin
  4. A reflection across the line y equals x

Explanation

Applying a 90-degree counterclockwise rotation about the origin sends (x, y) to (negative y, x). The rule matches this rotation exactly.

Question 37Geometry (Ohio's Learning Standards for Mathematics)

A rectangular garden measures 20 meters by 15 meters. A path of uniform width is built around it, increasing the outer dimensions to 24 meters by 19 meters. What is the area of the path in square meters?

  1. 456
  2. 300
  3. 120
  4. 156 Correct answer.

Explanation

The outer area is 24 times 19, which equals 456 square meters. The garden area is 20 times 15, which equals 300 square meters. The path area is the difference, 156 square meters.

Question 38Geometry (Ohio's Learning Standards for Mathematics)

A cone has a slant height of 13 centimeters and a base radius of 5 centimeters. What is the lateral surface area in square centimeters, expressed in terms of pi?

  1. 130 pi
  2. 25 pi
  3. 65 pi Correct answer.
  4. 90 pi

Explanation

The lateral surface area of a cone equals pi times the radius times the slant height. Multiplying pi by 5 by 13 gives 65 pi square centimeters.

Question 39Geometry (Ohio's Learning Standards for Mathematics)

Two triangles are congruent. Which statement about them must be true?

  1. They are both equilateral
  2. They have equal areas and equal perimeters Correct answer.
  3. They are both right triangles
  4. They are similar but not congruent

Explanation

Congruent triangles have corresponding parts equal, so all corresponding side lengths match and the perimeters and areas are equal. Congruence implies similarity, not the reverse.

Question 40Geometry (Ohio's Learning Standards for Mathematics)

A right triangle has legs of length 5 and 12. A similar right triangle has a hypotenuse of 39. What is the perimeter of the larger triangle?

  1. 60
  2. 84
  3. 78
  4. 90 Correct answer.

Explanation

The smaller hypotenuse is 13, so the similarity ratio is 39/13, which is 3. The larger legs are 15 and 36, and the perimeter is 15 plus 36 plus 39, which equals 90.

Question 41Geometry (Ohio's Learning Standards for Mathematics)

In a circle, two chords intersect inside the circle. One chord is divided into segments of length 4 and 9. If one segment of the other chord has length 6, what is the length of the other segment?

  1. 5
  2. 7
  3. 8
  4. 6 Correct answer.

Explanation

When two chords intersect, the products of their segment lengths are equal. So 4 times 9 equals 36, and 6 times the unknown segment equals 36, giving a length of 6.

Question 42Geometry (Ohio's Learning Standards for Mathematics)

An angle is formed by a tangent and a secant intersecting at the point of tangency on a circle. The intercepted arc measures 140 degrees. What is the measure of the angle in degrees?

  1. 140
  2. 70 Correct answer.
  3. 35
  4. 280

Explanation

An angle formed by a tangent and a chord at the point of tangency equals half the measure of its intercepted arc. Half of 140 is 70 degrees.

Question 43Geometry (Ohio's Learning Standards for Mathematics)

A right prism has a base that is a regular hexagon with side length 4. The prism has a height of 10. What is the volume of the prism in cubic units?

  1. 120 times the square root of 3
  2. 240 times the square root of 3 Correct answer.
  3. 480 times the square root of 3
  4. 60 times the square root of 3

Explanation

The area of a regular hexagon with side 4 is six times the area of an equilateral triangle of side 4, which is 24 times the square root of 3. Multiplying by the height of 10 gives 240 times the square root of 3.

Question 44Geometry (Ohio's Learning Standards for Mathematics)

A line passes through (1, 2) and is parallel to the line with equation y equals 3x minus 5. What is the y-intercept of this line?

  1. 3
  2. negative 1 Correct answer.
  3. 2
  4. 5

Explanation

Parallel lines share the same slope, so the new line has slope 3. Using the point-slope form with (1, 2) gives y equals 3x minus 1, so the y-intercept is negative 1.

Question 45Geometry (Ohio's Learning Standards for Mathematics)

A circle has a radius of 8. A sector of the circle has an area of 32 pi square units. What is the measure of the central angle of the sector in degrees?

  1. 120
  2. 45
  3. 180 Correct answer.
  4. 90

Explanation

The whole circle has area 64 pi. The sector's area of 32 pi is half the circle, so the central angle is half of 360 degrees, which is 180 degrees.

Question 46Geometry (Ohio's Learning Standards for Mathematics)

A triangle has vertices at (0, 0), (6, 0), and (0, 8). What is the length of the median drawn from the vertex at (0, 8) to the hypotenuse?

  1. 5 Correct answer.
  2. 6
  3. 4
  4. 10

Explanation

The triangle is right with legs 6 and 8 and hypotenuse 10. The midpoint of the hypotenuse is (3, 0), and the distance from (0, 8) to (3, 0) is the square root of 9 plus 64, which is 5. This equals half the hypotenuse, as expected.

Question 47Geometry (Ohio's Learning Standards for Mathematics)

A quadrilateral has vertices at (1, 1), (5, 1), (5, 4), and (1, 4). What is the perimeter of the quadrilateral?

  1. 12
  2. 16
  3. 20
  4. 14 Correct answer.

Explanation

The figure is a rectangle with width 4 and height 3. Its perimeter is twice the sum of the width and height, which is 2 times 7, or 14.

Question 48Geometry (Ohio's Learning Standards for Mathematics)

A sphere has a surface area of 100 pi square centimeters. What is the radius of the sphere in centimeters?

  1. 5 Correct answer.
  2. 10
  3. 25
  4. 50

Explanation

The surface area of a sphere is four pi times the square of the radius. Setting four pi r squared equal to 100 pi gives r squared equal to 25, so the radius is 5.

Question 49Geometry (Ohio's Learning Standards for Mathematics)

A dilation with center at the origin maps a triangle with area 12 square units to a triangle with area 108 square units. What is the scale factor of the dilation?

  1. 3 Correct answer.
  2. 9
  3. 6
  4. 2

Explanation

Under a dilation with scale factor k, areas are multiplied by k squared. Since 108 divided by 12 is 9, k squared equals 9 and k equals 3.

Question 50Geometry (Ohio's Learning Standards for Mathematics)

In a triangle, two angles measure 47 degrees and 68 degrees. What is the measure of the exterior angle at the third vertex?

  1. 65
  2. 245
  3. 115 Correct answer.
  4. 115 degrees is also the sum of the two given angles, confirming the result

Explanation

The third interior angle is 180 minus 47 minus 68, which equals 65 degrees. The exterior angle is supplementary to it, so it measures 115 degrees, which also equals the sum of the two remote interior angles.