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Angle Word Problems Practice Questions

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Updated on Oct 3, 2011

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

Angle Word Problems Practice Questions

Practice 1

Problems

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

Solutions

  1. acute
  2. complementary
  3. right
  4. obtuse
  5. 180 – 30 = 150

Practice 2

Problems

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

Angle Word Problems

      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

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

Solutions

  1. 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.
  2. Make a plan. Use the expressions given that represent each angle, set the expressions equal to each other, and solve for x.

    Carry out the plan. Let 6x = one angle and 2x + 80 = the other angle. The equation is 6x = 2x + 80. Subtract 2x from each side to get 4x = 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.

  3. 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°.
  4. 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 2x + 15 = 90. Subtract 15 from each side of the equation to get 2x = 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.

  5. 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°.
  6. 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 2x = the larger angle. Therefore, the equation isx+ 2x = 180. Combine like terms to get 3x= 180. Divide each side of the equation by 3 to get the variable alone:x= 60. Thus, 2x= 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.

  7. 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.
  8. 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 5x+ 10 = one angle and let 2x+ 55 = the other angle. The equation is 5x+ 10 = 2x+ 55. Subtract 2xfrom each side to get 3x+ 10 = 55. Subtract 10 from each side to get the equation 3x= 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.

  9. 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.
  10. 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 7x= one angle, and let 5x+ 40 = the other angle. The equation is 7x= 5x+ 40. Subtract 5xfrom each side to get 2x= 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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