Two complementary angles are such that two times the measure of one is equal to three times the measure of the other. The measure of the smaller angle is (a) `45^@` (b) `30^@` (c) `36^@` (d) none of these

Explanation

Let one angle be xº.
Then, the other complementary angle becomes `(90 - x)°`
It is given that two times the angle measuring `xº` is equal to three times the angle measuring `(90 - x)`
Or, we can say that:
`2x = 3(90-x)`
`2x = 270 - 3x`
`2x + 3x = 270`
`5x = 270`
On dividing both sides of the equation by `5`,we get
`270/ 5= x `
=`x = 54 `
Also, the other complementary angle becomes `90 -x`
= `90 -54`
= `36^@`