74 Chapter 2 Linear Equations and Inequalities in One Variable Solution 1c. The two angles form a straight angle and, therefore, have a sum of 180°. 5a + a = 180 Express the relationship. 6a = 180 Combine like terms. 6a 180 = 6 6 Divide each side by 6. a = 30 Simplify. So, one angle is 30° and the other angle is 5(30) = 150°. The check is left for the reader. 1d. The diagram illustrates two vertical angles. Find the measure of each angle. (9x – 6)° (7x + 2)° Solution 1d. Since the angles are vertical angles, their measures are equal. 9x - 6 = 7x + 2 Express the relationship. 9x - 6 - 7x = 7x + 2 - 7x Subtract 7x from each side. 2x - 6 = 2 Simplify. 2x - 6 + 6 = 2 + 6 Add 6 to each side. 2x = 8 Simplify. 2x 8 = 2 2 Divide each side by 2. x = 4 Simplify. Check: 9x - 6 = 7x +2 Begin with the original equation. 9(4) - 6 = 7(4) + 2 Replace x with 4. 36 - 6 = 28 + 2 Simplify. 30 = 30 True The measure of each angle is 30° because 9(4) - 6 = 30 and 7(4) + 2 = 30. Student Check 1 Find the measure of each unknown angle. 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 angles in the diagram make a straight angle. Find the measure of each angle. d. The diagram illustrates two vertical angles. Find the measure of each angle. a° (2a + 12)° Perimeter, Area, and Circumference Formulas An equation that describes a known relationship between quantities, such as distance, area, weight, and so forth, is called a formula. We can think of a formula as an equation with several variables. Formulas enable us to find valuable information about specific quantities. (2a + 10)° (3a – 40)° Objective 2 ▶ Use perimeter, area, and circumference formulas.
hendricks_intermediate_algebra_1e_ch1_3
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