Question

Recall that two angles are complementary if the sum of their measures is 90°. Find the measures of two complementary angles if one angle is 6º more than three times the other angle. ​

Answer 1

The two angles are 69° and 21°.

Explanation:

Write out the expression:

let x and y be two angles that are complementary and the sum of their measures is 90°

-> x° + y° = 90°

if one angle is 6º more than three times the other angle:

-> x° = 6° +3y°

Plug x = 6+3y into x° + y° = 90°

6° + 3y° + y° = 90°

Solve for y

4y° = 84°

y° = 21°

Plug y into x° + y° = 90°

x° + 21° = 90°

Solve for x°

x° = 90° - 21° = 69°