The degree measures of adjacent angles are proportional to the numbers 7 and 2. Find the larger of these angles.

1. ∠AOB and ∠BОС are adjacent. ∠AOB: ∠BОС = 7: 2. Therefore, ∠AOB = 7∠BОС / 2.

2. According to the property of adjacent angles, the total value of their degree measures is 180 °.

3. Using this property, we calculate the degree measures of these angles:

∠AOB + ∠BОС = 180 °.

4. Substitute 7∠BОС / 2 instead of ∠АОB into this expression:

7∠BОС / 2 + ∠BОС = 180 °. 9∠BОС / 2 = 180 °.

9∠BОС = 2 x 180 °.

∠BOC = 40 °.

∠AOB = 7 x 40/2 = 140 °.

AOB is the larger of the two given angles.

Answer: ∠AOB is the larger of the two given angles.