How to

Question

A geometric figure has angles with the following 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.

Answer 1

To determine which two angles are supplementary, we need to find two angles that add up to 180°.

Let's check the pairs of angles:

1. \( 34° + 105° = 139° \) (not supplementary)
2. \( 34° + 146° = 180° \) (supplementary)
3. \( 34° + 97° = 131° \) (not supplementary)
4. \( 105° + 146° = 251° \) (not supplementary)
5. \( 105° + 97° = 202° \) (not supplementary)
6. \( 146° + 97° = 243° \) (not supplementary)

From the calculations, we find that the angles \( 34° \) and \( 146° \) are supplementary because they add up to \( 180° \).

Thus, the smaller angle first and the larger angle second is:

34°, 146°.