Question

When angles are complementary the sum of their measures is 90 degrees. Two complementary angles have measured of 2x-10 degrees and 3x-10. Fine the measures of each angle

Answer 1

56° and 34°

complementary angles sum to 90° thus

3x - 10 + 2x - 10 = 90

5x - 20 = 90

add 20 to both sides of the equation

5x = 90 + 20 = 110

divide both sides by 5

x = $\frac{110}{5}$ = 22

angle 2x - 10 = (2 × 22) - 10 = 44 - 10 = 34° and

angle 3x - 10 = (3 × 22) - 10 = 66 - 10 = 56°