Let's solve the problem step-by-step.

Problem Statement

We need to find the measures of two angles using an algebraic equation. The measure of one angle is four times greater than its supplement. We will represent the degree measure of the angle's supplement as $x$.

Definitions

1. Supplementary Angles: Two angles are supplementary if their sum is $180^\circ$.
2. Given Condition: The measure of the angle is four times greater than its supplement.

Solution

1. Let:
   $x =$ measure of the supplement angle.

2. Angle:
   The other angle, which is four times greater than the supplement, is $4x$.

3. Equation:
   Since the two angles are supplementary, their sum is $180^\circ$. Thus, we have: $x + 4x = 180$

4. Combine Like Terms:
   $5x = 180$

5. Solve for $x$:
   $x = \frac{180}{5} = 36$

6. Determine the Other Angle:
   The other angle is $4x$: $4 \times 36 = 144$

Final Result

• Supplement Angle: $36^\circ$
• Other Angle: $144^\circ$

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Related Questions

1. What are complementary angles, and how do they differ from supplementary angles?
2. Can you have negative angles as supplements?
3. What would be the measure of each angle if the condition was “the measure of the angle is twice its supplement”?
4. How can you find the complement of an angle?
5. How are angles used in trigonometric functions?

Tip

Always remember that the sum of supplementary angles is $180^\circ$ and complementary angles is $90^\circ$.