Section 2.3 Formulas and Applications 73 We use the angle relationships involving complementary, supplementary, and vertical angles to solve the problems in Example 1. We write a corresponding linear equation that represents the situation and then we solve it. Objective 1 Examples Find the measure of each unknown angle. 1a. Find the measure of an angle whose complement is 15° less than twice the measure of the angle. Solution 1a. What is unknown? The measures of an angle and its complement are unknown. Let a represent the measure of the angle. Then 90 - a represents the measure of the complement. To write the equation, we use the following statement. 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 3a = 3 3 Divide each side by 3. 35 = a Simplify. So, the measure of the angle is 35°. The check is left for the reader. 1b. Find the measure of an angle whose supplement is 40° more than the measure of the angle. Solution 1b. What is unknown? The measures of an angle and its supplement are unknown. Let a represent the measure of the angle. Then 180 - a represents the measure of the supplement. To write the equation, use the following statement. Supplement is 40° more than the measure of the angle. 180 - a = a + 40 Express the relationship. 180 - a + a = a + 40 + a Add a to each side. 180 = 2a + 40 Simplify. 180 - 40 = 2a + 40 - 40 Subtract 40 from each side. 140 = 2a Simplify. 140 2a = 2 2 Divide each side by 2. 70 = a Simplify. So, the measure of the angle is 70°. The check is left for the reader. 1c. The following angles make a straight angle. Find the measure of each angle. (5a)° a°
hendricks_intermediate_algebra_1e_ch1_3
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