Answer:
The measure of the angle is <u>64</u> degree.
The measure of the supplement is <u>116</u> 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
and 12 less means 12 is subtracted from
.
So, supplement of the angle = ![2x-12](https://tex.z-dn.net/?f=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](https://tex.z-dn.net/?f=x%2B2x-12%3D180)
⇒ ![3x-12=180](https://tex.z-dn.net/?f=3x-12%3D180)
⇒ ![3x=180+12](https://tex.z-dn.net/?f=3x%3D180%2B12)
⇒ ![3x=192](https://tex.z-dn.net/?f=3x%3D192)
⇒ ![x=\frac{192}{3}=64\°](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B192%7D%7B3%7D%3D64%5C%C2%B0)
The measure of the supplement = ![2(64)-12=128-12=116](https://tex.z-dn.net/?f=2%2864%29-12%3D128-12%3D116)
The measure of the angle is <u>64</u> degree.
The measure of the supplement is <u>116</u> degree.