12) The measures of two supplementary angles have a ratio of $$ 4: 5 $$. What is the measure of the larger angle? The measure of the larger angle is

Question

UpStudy AI · Accepted Answer

To find the measure of the larger supplementary angle with a ratio of $$ 4:5 $$, follow these steps:

1. **Understand Supplementary Angles:**
   - Supplementary angles add up to **180 degrees**.

2. **Set Up the Ratio:**
   - Let the two angles be $$ 4x $$ and $$ 5x $$, where $$ x $$ is a common multiplier.

3. **Create the Equation:**
   $$
   4x + 5x = 180
   $$
   
4. **Solve for $$ x $$:**
   $$
   9x = 180 \
   x = \frac{180}{9} \
   x = 20
   $$

5. **Find the Larger Angle:**
   - The larger angle is $$ 5x $$:
   $$
   5x = 5 \times 20 = 100 \text{ degrees}
   $$

**Answer:** The measure of the larger angle is **100 degrees**.
The larger angle measures **100 degrees**.

12) The measures of two supplementary angles have a ratio of \( 4: 5 \). What is the measure of the larger angle? The measure of the larger angle is