Question

The measure of the supplement of an angle is 12° less than twice the measure of the angle. What is the measurement, in degrees, of the angle and its supplement?

​The measurement of the angle is ______ degrees.

​The measurement of the supplement is ______ degrees.

Answer 1

The measure of the angle is 64 degree.

The measure of the supplement is 116 degree.

Explanation:

Let the measure of the angle be 'x'.

Given:

Supplement of the angle is 12 less than twice the measure of the angle.

Twice the angle means 2 times of the angle which is
`2x` and 12 less means 12 is subtracted from
`2x`.

So, supplement of the angle =
`2x-12`

Now, by definition of supplementary angles, if two angles are supplement of one another, then their sum is 180 degrees.

Therefore, the sum of the given angles = 180°

⇒
`x+2x-12=180`

⇒
`3x-12=180`

⇒
`3x=180+12`

⇒
`3x=192`

⇒
`x=(192)/(3)=64\°`

The measure of the supplement =
`2(64)-12=128-12=116`

The measure of the angle is 64 degree.

The measure of the supplement is 116 degree.