2025 · Q84
A Question is given followed by two Statements I and II.
Question: In triangle ABC, ∠A = ∠B - ∠C. Is angle A acute?
Statement IABC is not obtuse-angled.
Statement IIAngle C is acute.
Which one of the following is correct?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
- BThe Question can be answered by using either Statement alone
- CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
- DThe Question can be answered even without using any of the Statements
Explanation
angle A = angle B - angle C gives angle B = angle A + angle C, so 2(angle A + angle C)=180 degrees, i.e. angle B=90 and angle A<90 - A is acute with no statements at all. The statements are redundant.