Question

The measure of an angle is eight times the measure of it’s supplementary angle.what is the measure of each angle?

Answer 1

The measure of the supplementary angles are
`160^(0)` and
`20^(0)`.

Explanation:

Two angles, measuring less than or equal to
`180^(0)`, are said to supplementary if their sum is
`180^(0)`.

Let us suppose that the measure of one angle is
`x^(0)`.

Then the measure of other angle is,
`(180^(0) -x^(0))`.

It is provided that the measure of an angle is eight times the measure of it’s supplementary angle, that is

`x^(0) =8(180^(0) -x^(0))`

Solving this equation for
`x^(0)`,

`x^(0) =8(180^(0) -x^(0))\\x^(0) =1440^(0) -8x^(0)\\9x^(0)=1440\\x^(0)=160^(0)`

So the measure of one angle is
`160^(0)`.

Then the measure of the other angle is,

`180^(0) -x^(0) = 180^(0) -160^(0) \\=20^(0)`

Therefore, the measure of the supplementary angles are
`160^(0)` and
`20^(0)`.