Difficulty: Medium
Correct Answer: 60°
Explanation:
Introduction / Context:Angle relations given as equalities allow expressing each angle in terms of a common parameter and then using the triangle sum property (180°).
Given Data / Assumptions:
Concept / Approach:Express A, B, C via k and substitute into A + B + C = 180° to solve for k, then A.
Step-by-Step Solution:
A = k/2, B = k/3, C = k/6A + B + C = k(1/2 + 1/3 + 1/6) = k(1) = 180°k = 180° ⇒ A = k/2 = 90°But check: 2A = 180°, 3B = 180°, 6C = 180° ⇒ A = 90°, B = 60°, C = 30°.Verification / Alternative check:Sum 90° + 60° + 30° = 180° ✓, and the proportional relations hold.
Why Other Options Are Wrong:
Common Pitfalls:Confusing 2A = 3B = 6C with A:B:C directly; not converting each to k-based expressions first.
Final Answer:90°
Discussion & Comments