Section 2.5 Formulas and Applications from Geometry 143 4b. What is unknown? The measure of the angle and its supplement are unknown. Let a = the measure of the angle. Then 180 - a = the measure of the supplement. What is known? The supplement is 40° more than the measure of the angle. We use this statement to write the equation that we will use to solve the problem. Supplement is 40° more than the measure of the angle. 180 - a = a + 40 Express the relationship. Add a to each side. Simplify. Subtract 40 from each side. Simplify. Divide each side by 2. Simplify. 180 - a + a = a + 40 + a 180 = 2a + 40 180 - 40 = 2a + 40 - 40 140 = 2a 140 2 = 2a 2 70 = a So, the measure of the angle is 70°. 4c. What is unknown? The measure of the angle, its complement and supplement are unknown. Let a = the measure of the angle. Then 90 - a = the measure of the complement and 180 - a = the measure of the supplement. What is known? The supplement of an angle is 10° more than twice its complement. We use this relationship to write the equation to solve the problem. Supplement is 10° more than twice its complement. 180 - a = 2(90 - a) + 10 Express the relationship. Apply the distributive property. Combine like terms on the right. Add 2a to each side. Simplify. Subtract 180 from each side. Simplify. 180 - a = 180 - 2a + 10 180 - a = 190 - 2a 180 - a + 2a = 190 - 2a + 2a 180 + a = 190 180 + a - 180 = 190 - 180 a = 10 So, the measure of the angle is 10°. Student Check 4 Find the measure of each unknown angle. Write an equation that represents the situation and solve it. a. Find the measure of an angle whose complement is 10° more than three times the angle. b. Find the measure of an angle whose supplement is 60° more than the angle. c. The supplement of an angle is 30° more than twice its complement. Find the measure of the angle. Straight and Vertical Angles As mentioned in Objective 4, straight angles are angles whose measure is 180°. Straight angles form a straight line. Objective 5 ▶ Solve problems involving straight and vertical angles.
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