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 unknowns. Then 7x 4 represents the measure of the other angle. The angles are complementary, so the sum of their measures must be . second anglea b Measure of a 90° measure of Step 3: Write a verbal model. x 7x 4 90 Step 4: Write a mathematical equation. Step 5: Solve for x. Step 6: Interpret the results and 8x 4 90 8x 86 8x 8 86 8 One measure is . write the answer in words. The other measure is 7x 4 7110.752 4 79.25 . The measures of the angles are and . Solving a Geometry Application Involving Angles in a Triangle One angle in a triangle is twice as large as the smallest angle. The third angle is 10º 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 unknowns. Then 2x and 7x 10 represent the measures of the other two angles. (7x 10) x° (2x) Example 5 10.75° 79.25° x 10.75 x 10.75 first angle b 90° 4° Example 4 Section 2.6 Literal Equations and Applications of Geometry 167 Skill Practice 5. Two complementary angles are constructed so that one measures less than six times the other. Find the measures of the angles. 80° Classroom Example: p. 171, Exercise 58 (7x 4)° x° The sum of the measures must be 180°. Classroom Example: p. 171, Exercise 52 Answers 5. 13° and 77° 6. 25°, 50°, and 105° 1° Skill Practice 6. In a triangle, the measure of the first angle is greater than the measure of the second angle. The measure of the third angle is twice that of the second. Find the measures of the angles.
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