In △ABC, if 2∠A = 3∠B = 6∠C, find the measure of ∠A.

Difficulty: Medium

60°
30°
90°
120°

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:

2A = 3B = 6C = k (some common value).
A + B + C = 180°.

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:

60°, 120°, 30° do not match the derived A = 90°.

Common Pitfalls:
Confusing 2A = 3B = 6C with A:B:C directly; not converting each to k-based expressions first.

In △ABC, if 2∠A = 3∠B = 6∠C, find the measure of ∠A.

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