Question

find the angle,if its complement is one fourth of its supplement.

Answer 1

Let angle to found = x
Then complement = y = 90 - x
Supplement = = z = 1/4 *y = 180 - x

Given, complement = 1/4 * supplement
Replacing values in equation,

4y = z (complement one-fourth of supplement)

4(90 - x) = 180 - x
360 - 4x = 180 - x
360 - 180 = 4x - x
180 = 3x
x = 180/3
x = 60 degrees

Answer: 60 degrees

Verification:

If x = 60, complement = 90 - x = 90 - 60 = 30
supplement = 180 - x = 180 - 60 = 120

complement should be = to 1/4 * supplement
30 = 1/4 * 120
30 = 30

So, the answer is correct.

Hope you got what you needed.

Answer 2

complement of x=90-x
supplement of x=180-x
90-x=1/4(180-x)
90-x=45-x/4
90-45=x+x/4
45=4x/4+x/4
45=5x/4
therefore x=45*4/5
                   =36