Question

Two angles are complementary. The measure of the larger angle is 26 degrees less than 3 times the measure of the smaller angle. The measure of the smaller angle is ________ degrees, and the larger angle is ________ degrees.

Answer 1

smaller angle = 29°

larger angle = 61°

Explanation:

Let x be the larger angle and y be the smaller angle

Larger angle is 26° less than 3 times the smaller angle

i. e x = 3y-26°

Since x and y are complementary angles, we can write,

x + y = 90°

or, (3y - 26°) + y = 90°

or, 4y = 90° + 26°

or, y = 116°/4

or, y = 29°

So,

x = 3 * 29° - 26° = 61°

Answer 2

29, 61

Explanation:

x = smaller

y = larger

y = 3x - 26

x + y = 90

x + 3x - 26 = 90

4x - 26 = 90

4x = 116

x = 29

x + y = 90

29 + y = 90

y = 90 - 29

y = 61