To review these concepts, go to Angle Word Problems Study Guide.

## Angle Word Problems Practice Questions

**Practice 1**

**Problems**

- The measure of an angle is 31°. This angle is classified as an _____ angle.
- The sum of the measures of two angles is exactly 90°. These are known as a pair of __________ angles.
- One angle with a measure of 90° is known as a _______ angle.
- An angle with a degree measure between 90° and 180° is an _________ angle.
- If one angle of a linear pair is 30°, then the measure of the other angle in the pair is ________ °.

**Solutions**

- acute
- complementary
- right
- obtuse
- 180 – 30 = 150

**Practice 2**

**Problems**

Using the following figure, find the measure of each angle.

*m*1 = _____

*m*2 = _____

*m*3 = _____

*m*4 = _____

*m*5 = _____

*m*6 = _____

**Solutions**

- m1 = __ 140 __

- m2 = __ 140 __

- m3 = __ 40 __

- m4 = __ 140 __

- m5 = __ 140 __

- m6 = __ 40 __

**Practice 3**

**Problems**

- The measures of two vertical angles are expressed as 6
*x*and 2*x*+ 80. What is the measure in degrees of each angle? - The measure of an angle is 15 more than its complement. What is the measure in degrees of both angles?
- The measure of an angle is twice the measure of its supplement. What is the measure in degrees of both angles?
- The measure of two alternate exterior angles formed by two parallel lines cut by a transversal are expressed as 5
*x*+ 10 and 2*x*+ 55. What is the number of degrees in each angle? - Two parallel lines are cut by a transversal. A pair of corresponding angles is represented by the expressions 7
*x*and 5*x*+ 40. What is the measure of each angle?

**Solutions**

*Read and understand the question*. This question is looking for the measure of each vertical angle. The vertical angles formed by two intersecting lines are always congruent.*Read and understand the question*. This question is looking for the measure of each complementary angle. The sum of the measures of two complementary angles is always 90°.*Read and understand the question*. This question is looking for the measure of each supplementary angle. The sum of the measures of two supplementary angles is always 180°.*Read and understand the question*. This question is looking for the measure of each alternate exterior angle. The alternate exterior angles formed by two parallel lines cut by a transversal are congruent.*Read and understand the question*. This question is looking for the measure of each corresponding angle. The corresponding angles formed by two parallel lines cut by a transversal are congruent.

*Make a plan*. Use the e*x*pressions given that represent each angle, set the e*x*pressions equal to each other, and solve for *x*.

*Carry out the plan*. Let 6*x* = one angle and 2*x* + 80 = the other angle. The equation is 6*x* = 2*x* + 80. Subtract 2*x* from each side to get 4*x* = 80. Then, divide each side by 4 to get the variable alone: *x* = 20. Therefore, the angles are 6(20) = 120° each.

*Check your answer*. To check this solution, substitute *x* = 20 into the other expression to be sure it also is equal to 120°: 2(20) + 80 = 40 + 80 = 120°. Each vertical angle is 120°, so this answer is checking.

*Make a plan*.Write the expression for each angle and set the sum equal to 90. *Carry out the plan*. Let *x*= the smaller angle, and let *x*+ 15 = the larger angle. Therefore, the equation is *x*+*x*+ 15 = 90. Combine like terms to get 2*x* + 15 = 90. Subtract 15 from each side of the equation to get 2*x* = 75. Divide each side of the equation by 2 to get the variable alone: *x*= 37.5. Thus, *x*+ 15 = 52.5. The two angles measure 37.5° and 52.5°, respectively. *Check your answer*. To check this problem, make sure that the sum of the measures of the angles is equal to 90° and that one angle is 15 more than the other. The angles are 37.5 + 52.5 = 90° and 52.5 – 37.5 = 15, so this problem is checking.

*Make a plan*.Write the expression for each angle and set the sum equal to 180. *Carry out the plan*. Let *x* = the smaller angle, and let 2*x* = the larger angle. Therefore, the equation is*x*+ 2*x* = 180. Combine like terms to get 3*x*= 180. Divide each side of the equation by 3 to get the variable alone:*x*= 60. Thus, 2*x*= 120. The two angles measure 60° and 120°, respectively. Check your answer. To check this problem, make sure that the sum of the measures of the angles is equal to 180° and that one angle is twice the other. The angles are 60 + 120 = 180° and (60)(2) = 120, so this answer is checking.

*Make a plan*. Use the expressions that represent each angle. Set the expressions equal to each other and solve for *x*.

*Carry out the plan*. Let 5*x*+ 10 = one angle and let 2*x*+ 55 = the other angle. The equation is 5*x*+ 10 = 2*x*+ 55. Subtract 2*x*from each side to get 3*x*+ 10 = 55. Subtract 10 from each side to get the equation 3*x*= 45. Then, divide each side of the equation by 3 to get the variable alone:*x*= 15. Therefore, the angles are 5(15) + 10 = 75 + 10 = 85° each.

*Check your answer*. To check this solution, substitute *x*= 15 into the other expression to be sure it also is equal to 85°: 2(15) + 55 = 30 + 55 = 85°. Each alternate exterior angle is 85°, so this solution is checking.

*Make a plan*. Use the expressions that represent each angle. Set the expressions equal to each other, and solve for *x*.

*Carry out the plan*. Let 7*x*= one angle, and let 5*x*+ 40 = the other angle. The equation is 7*x*= 5*x*+ 40. Subtract 5*x*from each side to get 2*x*= 40. Divide each side of the equation by 2 to get the variable alone: *x*= 20. Therefore, the angles are 7(20) = 140° each.

*Check your answer*. To check this solution, substitute *x*= 20 into the other expression to be sure it also is equal to 140°: 5(20) + 40 = 100 + 40 = 140°. Each corresponding angle is 140°, so this solution is checking.

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