Find the measure of an angle if its measure is 20° less than its supplement.

Let the measure of the angle be \( x \). The supplement of an angle is the difference between 180° and the angle itself. Therefore, the supplement of \( x \) is \( 180^\circ - x \).

According to the problem, the measure of the angle is 20° less than its supplement. So, we set up the equation:

\[
x = (180^\circ - x) - 20^\circ
\]

Now, solve for \( x \):

\[
x = 160^\circ - x
\]

Add \( x \) to both sides:

\[
2x = 160^\circ
\]

Divide both sides by 2:

\[
x = 80^\circ
\]

Thus, the measure of the angle is \( 80^\circ \).

Would you like further details on solving linear equations or anything else? Here are 5 related questions you can explore:

1. What is the supplement of an 80° angle?
2. How do you find the complement of an angle?
3. What is the relationship between complementary and supplementary angles?
4. Can an angle and its supplement ever be equal? Why or why not?
5. What is the measure of an angle if it is 30° less than its supplement?

**Tip:** For any angle \( \theta \), the supplementary angle can always be found using the formula \( 180^\circ - \theta \).

Learn how to find the measure of an angle that is 20° less than its supplement using algebra. This step-by-step solution explores supplementary angles and how to solve the equation for the unknown angle. Suitable for students in Grades 7-9.

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