Two angles are supplementary. The measure of one angle is four times the measure of the other angle. Write and solve an algebraic equation to find the measure of each angle based on the given description.

Let's define the two angles as follows:

- Let \( x \) represent the measure of the smaller angle.
- The other angle, being four times larger, will be \( 4x \).

Since the two angles are supplementary, their measures must add up to 180°. Therefore, we can set up the following equation:

\[
x + 4x = 180
\]

### Step 1: Simplify the equation.
\[
5x = 180
\]

### Step 2: Solve for \( x \).
\[
x = \frac{180}{5} = 36
\]

So, the smaller angle is \( 36^\circ \).

### Step 3: Find the measure of the larger angle.
Since the larger angle is four times the smaller angle:
\[
4x = 4 \times 36 = 144
\]

Thus, the two angles are:
- Smaller angle: \( 36^\circ \)
- Larger angle: \( 144^\circ \)

Would you like more details or have any questions about this solution?

Here are some related questions:
1. What if the larger angle was three times the smaller one?
2. How would the equation change if the angles were complementary instead of supplementary?
3. Can two acute angles be supplementary? Why or why not?
4. What if the sum of two angles was 90° instead of 180°?
5. How can you verify the angles are indeed supplementary?

**Tip:** Remember, supplementary angles always add up to \(180^\circ\), while complementary angles add up to \(90^\circ\).

This problem explores how to solve for two supplementary angles where one is four times the other. Step-by-step, we use algebraic equations to determine the measures of the angles, suitable for students in Grades 6-8.

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