150 Chapter 2 Linear Equations and Inequalities Solving a Geometry Application Involving Complementary Angles Two complementary angles are drawn such that one angle is more than seven times the other angle. Find the measure of each angle. Solution: Step 1: Read the problem. Let x represent the measure of one angle. Step 2: Label the variables. Then 7x 4 represents the measure of the other angle. The angles are complementary, so their sum must be . a 90° measure of second angle Step 3: Write a verbal model. x 7x 4 90 Step 4: Write a mathematical equation. Step 5: Solve for x. 8x 4 90 8x 86 8x 8 x 10.75 One angle is . Step 6: Interpret the results and write the answer in words. x 10.75 7x 4 7110.752 4 79.25 The other angle is . The angles are and . Skill Practice 5. Two complementary angles are constructed so that one measures less than six times the other. Find the measures of the angles. Solving a Geometry Application Involving Angles in a Triangle Example 5 One angle in a triangle is twice as large as the smallest angle. The third angle is 10° more than seven times the smallest angle. Find the measure of each angle. Solution: Step 1: Read the problem. Let x represent the measure of the smallest angle. Step 2: Label the variables. Then 2x and 7x 10 represent the measures of the other two angles. The sum of the angles must be 180°. 1° 10.75° 79.25° 86 8 aMeasure of b b first angle 90° 4° Example 4 (7x 4)° x° Answer 5. The angles are 13° and 77°. (7x 10) x° (2x)
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