Complementary and Supplementary Angles Recall from Chapter 1 that complementary angles are angles whose sum is 90° and supplementary angles are angles whose sum is 180°. A 40° angle and 50° degree angle are complementary because their sum is 90°. The two angles together form a right angle. A right angle is an angle whose measure is 90°. A 40° angle and 140° degree angle are supplementary because their sum is 180°. The two angles together form a straight angle. A straight angle is an angle whose measure is 180°. Some other examples of complementary and supplementary angles are listed in the table. Complementary Angles Supplementary Angles 20°, 90° - 20° = 70° 20°, 180° - 20° = 160° 34°, 90° - 34° = 56° 34°, 180° - 34° = 146° 45°, 90° - 45° = 45° 45°, 180° - 45° = 135° 73°, 90° - 73° = 17° 73°, 180° - 73° = 107° x°, (90 - x)° y°, (180 - y)° In Section 2.1, we practiced setting up equations given information about complementary and supplementary angles. In this section, we will go through the entire process: setting up the equation and solving it. �� ������������������������ ������������������ Find the measure of each unknown angle. Write an equation that represents the situation and solve it. 4a. Find the measure of an angle whose complement is 15° less than twice the measure of the angle. 4b. Find the measure of an angle whose supplement is 40° more than the measure of the angle. 4c. The supplement of an angle is 10° more than twice its complement. Find the measure of the angle. Solutions 4a. What is unknown? The measure of the angle and its complement are unknown. Let a = the measure of the angle. Then 90 - a = measure of the complement. What is known? The complement is 15° less than twice the measure of the angle. We use this statement to write the equation that we will use to solve the problem. Complement is 15° less than twice the measure of the angle. 90 - a = 2a - 15 Express the relationship. 90 - a + a = 2a - 15 + a Add a to each side. 90 = 3a - 15 Simplify. 90 + 15 = 3a - 15 + 15 Add 15 to each side. 105 = 3a Simplify. 105 3 = 3a 3 Divide each side by 3. 35 = a Simplify. So, the measure of the angle is 35°. Objective 4 ▶ Solve problems involving complementary and supplementary angles. 40° 50° 140° 40° 142 Chapter 2 Linear Equations and Inequalities in One Variable
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