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

Answer:

The measure of the angle is 64 degree.

The measure of the supplement is 116 degree.

Step-by-step 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°

⇒ $x+2x-12=180$

⇒ $3x-12=180$

⇒ $3x=180+12$

⇒ $3x=192$

⇒ $x=\frac{192}{3}=64\°$

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.