Question

find the measure of the angle which is one fourth of its complement

Answer 1

let the angle be X.

ATP,
X= ¼(90-X)
=> 4X = 90 - X
=> 5X = 90
=> X = 18

Answer 2

The angle is 18 and its compliment is 72.

Solution:

Let us assume the angle is x and y is the compliment.

$x + y =90$ …………………. (i)

Again, the angle is one fourth of its compliment,

$x = \frac{1}{4}\times y$  

$4x = y$…………… (ii)

Substituting value of (ii) in (i) we get,

$(x +4x) =90$

$5x = 90$

$x = 18$

So, the angle is 18 and compliment is 72 .