To solve the problem of finding the measure of an angle whose measure is 20 less than the measure of its supplement, let's go through the steps systematically.
1. Understanding the Problem:
- Let the measure of the unknown angle be [tex]\( x \)[/tex].
- The supplement of this angle is [tex]\( 180^\circ - x \)[/tex] because the sum of an angle and its supplement always equals [tex]\( 180^\circ \)[/tex].
2. Set Up the Equation:
According to the problem, the measure of the angle [tex]\( x \)[/tex] is 20 degrees less than its supplement. Therefore, we can write the equation:
[tex]\[
x = (180^\circ - x) - 20^\circ
\][/tex]
3. Solve the Equation:
Now, we solve for [tex]\( x \)[/tex].
[tex]\[
x = 180^\circ - x - 20^\circ
\][/tex]
Combine like terms:
[tex]\[
x + x = 180^\circ - 20^\circ
\][/tex]
Simplify:
[tex]\[
2x = 160^\circ
\][/tex]
Divide both sides by 2:
[tex]\[
x = \frac{160^\circ}{2}
\][/tex]
[tex]\[
x = 80^\circ
\][/tex]
4. Conclusion:
The measure of the angle is [tex]\( 80^\circ \)[/tex].
Thus, the correct answer is:
C. 80
