Question

A geometric figure has angles with measurements 34, 105, 146, 97. Which two angle measure correspond to a supplementary pair? List the measure of the smaller angle first and the measure of the larger angle second.

Smaller angle: _____

Larger angle:______

Answer 1

To find the supplementary pair of angles, we need to check which pair of angles add up to 180 degrees.

Let's check the pairs:

1. **34 and 146**:
\[
34 + 146 = 180 \quad \text{(supplementary)}
\]

2. **105 and 97**:
\[
105 + 97 = 202 \quad \text{(not supplementary)}
\]

3. **34 and 97**:
\[
34 + 97 = 131 \quad \text{(not supplementary)}
\]

4. **105 and 146**:
\[
105 + 146 = 251 \quad \text{(not supplementary)}
\]

5. **34 and 105**:
\[
34 + 105 = 139 \quad \text{(not supplementary)}
\]

6. **146 and 97**:
\[
146 + 97 = 243 \quad \text{(not supplementary)}
\]

The only pair that adds up to 180 degrees is 34 and 146.

So:

Smaller angle: **34**

Larger angle: **146**