Question

find the measure of an angle which is 1)two third of its complement
2) four times of complement

Answer 1

Let the angle be x, then it's complement is 90 - x

1) According to the question,
x = 2/3 ( 90 - x)
x =60 - 2/3x
x + 2/3x = 60
(3x + 2x)/3 = 60
5x = 180
x = 36°
The angle is 36°

2) According to the question,
x = 4( 90 - x)
x = 360 - 4x
x + 4x = 360
5x = 360
x = 72°
The angle is 72°