**Supplementary Angles**

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

ExampleOne 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 2*x* + 50 = 180. Subtract 50 from each side of the equation to simplify it to 2*x* = 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.

ExampleWhen 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 3*x* – 60 = the other angle. The equation is *x* = 3*x* – 60. Add 60 to each side of the equation to get *x* + 60 = 3*x*. Subtract *x* from each side to get 60 = 2*x*. 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.

ExampleTwo 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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