In △ABC, if A − B = 15° and B − C = 30°, find the measure of ∠A.

Introduction / Context:Angles in a triangle relate via differences given. Convert them to expressions in one variable, then apply A + B + C = 180° to solve.

Given Data / Assumptions:

• A − B = 15° ⇒ A = B + 15°.
• B − C = 30° ⇒ C = B − 30°.
• A + B + C = 180°.

Concept / Approach:Substitute the expressions for A and C into the sum of angles and solve for B, then get A.

Step-by-Step Solution:

Verification / Alternative check:C = B − 30° = 35°. Check sum: 80° + 65° + 35° = 180° ✓, and differences match the givens.

Why Other Options Are Wrong:75°, 85°, 65° are values of other angles or near-misses; only 80° satisfies all constraints for A.

Common Pitfalls:Sign errors when expressing C, or forgetting to add all three angles to 180° in the final step.

Final Answer:80°