Question

Two angles are complementary. The sum of the measure of the first angle and one-fourth the second angle is 58.5 degrees. What are the measures of the small and large angle?

Answer 1

Let the angles be `theta and phi`.

Complementary angles are those whose sum is `90^@`.

It is given that `theta and phi` are complementary .
`implies theta+phi=90^@` `...........(i)`

The sum of the measure of the first angle and one-fourth the second angle is 58.5 degrees can be written as a equation.

`theta+1/4phi=58.5^@`

Multiply both sides by `4`.

`implies 4theta+phi=234^@`

`implies 3theta+theta+phi=234^@`

`implies 3theta+90^0=234^@`

`implies 3theta=144^@`

`implies theta=48^@`

Put `theta=48^@` in `(i)`

`implies 48^@+phi=90^@`

`implies phi=42^@`

Therefore, the small angle is `42^@` and larger angle is `48^@`