In △ABC, if A − B = 15° and B − C = 30°, find the measure of ∠A.
Aptitude
Plane Geometry
Difficulty: Medium
Choose an option
-
A65°
-
B80°
-
C75°
-
D85°
Answer
Correct Answer: 80°
Explanation
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:
(B + 15°) + B + (B − 30°) = 180°3B − 15° = 180°3B = 195° ⇒ B = 65°A = B + 15° = 80°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°