Problem 45 (9-10 : mk-2021-9-10-15)

Question The figure shows a semicircle with center 0. Two of the angles are given. What is the size, in degrees, of the angle \alpha?

Options

A: 9°

B: 11°

C: 16°

D: 17.5°

E: 18°

LLM Response: The angle α is an inscribed angle of the semicircle, so it must be half the measure of the central angle that has α as its minor arc. The central angle opposite to the given angles 32° and 67° measures 99° (since the sum of the angles in a triangle is 180°). Therefore, the measure of angle α is (99° / 2) = 49.5°. The answer is D4.

Final Prediction: Puzzle #45: Solve this question with explanation of the intermediate steps. Your response must end with one of the selected answer options from A1, B2, C3, D4, or E5. The figure shows a semicircle with center 0. Two of the angles are given. What is the size, in degrees, of the angle \alpha? Options: A1: 9°, B2: 11°, C3: 16°, D4: 17.5°, E5: 18°. Predicted Answer = D Correct Answer = A