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.

Question

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