Question

An angle is 32 more than one half of its complement .find the angle in degrees.

Answer 1

let x is one angle

x=(90-x)/2 +32

x-32=(90-x)/2

2x-64= 90-x

3x=90+64=154

x=154/3 and second (90-154/3)=(270-154)/3
=116/3

hence 154/3 and 116/3 are two angles

Answer 2

Let the complement be x
Then the angle = 1/2x + 32

A/Q,
x + 1/2x + 32 = 90 ..........since the angles are complementary
(2x + x)/2 = 90 - 32
3/2x = 58
x = 58 x  2/3
x = 116/3°

The required angle = 1/2 x 116/3 + 32 = 58/3 + 32 = 154/3°