Question

Two angles are complementary. The larger angle is 16 degrees larger than the smaller angle. Find the measure of both angles?

Answer 1

`color(brown)(hat A = 53^@, hat B = 37^@`

Explanation:

Two angles are said to be complementary, if their sum equals `90^@`

Let the two angles be `hat A, hatB`

Given `hat A + hat B = 90^@` Eqn (1)

Also given `hat A = hat B + 16`

Substituting value of `hat A` in terms of `hat B` in Eqn (1),

`(hat B + 16) + hat B= 90`

`2 hat B = 90 - 16 74`

`hat B = 74 / 2 = color (brown)(37^@`

Substituting value of `hat B` in Eqn (1),

`hat A = 90 - 37 = color(brown)(53^@`