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Angle Word Problems Study Guide (page 3)

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Updated on Oct 3, 2011

Supplementary Angles

Supplementary angle problems can be solved by adding the values of the angles and setting the sum equal to 180°.

Example

One of two supplementary angles measures 50° more than the other measures. What is the measure in degrees of each angle?

Read and understand the question. This question is looking for the measure of each supplementary angle. The measure of two supplementary angles is always 180°.

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 x + 50 = the larger angle. Therefore, the equation is x + x + 50 = 180. Combine like terms to get 2x + 50 = 180. Subtract 50 from each side of the equation to simplify it to 2x = 130. Divide each side of the equation by 2 to get the variable alone: x = 65. Thus, x + 50 = 115. The two angles measure 65° and 115°, 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 50° more than the other. The angles are 65 + 115 = 180°, and 115 – 65 = 50, so this answer is checking.

Alternate Interior and Alternate Exterior Angles

Alternate interior and alternate exterior angle problems can be solved by setting the values for each angle equal to each other.

Example

When parallel lines are cut by a transversal, the measure of one alternate interior angle is equal to 60 less than 3 times the other. Find the measure of both angles.

Read and understand the question. This question is looking for the measure of each alternate interior angle. The alternate interior angles formed by two parallel lines cut by a transversal are congruent.

Make a plan. Write an expression to represent each angle. Then, set the expressions equal to each other and solve for x.

Carry out the plan. Let x = one angle and 3x – 60 = the other angle. The equation is x = 3x – 60. Add 60 to each side of the equation to get x + 60 = 3x. Subtract x from each side to get 60 = 2x. Then, divide each side of the equation by 2 to get the variable alone: x = 30. Therefore, the angles are 30° each.

Check your answer. To check this solution, substitute x = 30 into the other expression to be sure it also is equal to 30°: 3(30) – 60 = 90 – 60 = 30°. Each alternate interior angle is 30°, so this answer is checking.

Corresponding Angles

Corresponding angle problems can be solved by setting the values for each angle equal to each other.

Example

Two parallel lines are cut by a transversal. The sum of two corresponding angles formed is 110°. What is the measure in degrees of each angle?

Read and understand the question. This question is looking for the measure of each corresponding angle. When parallel lines are cut by a transversal, the measures of corresponding angles are equal.

Make a plan. Take the given sum and divide by 2.

Carry out the plan. 110° divided by 2 is 55°. Each corresponding angle is 55°.

Check your answer. To check this solution, make sure that the sum of the two angles is 110°: 55 + 55 = 110, so this answer is checking.

Find practice problems and solutions for these concepts at Angle Word Problems Practice Questions.

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