Question: In a triangle ABC, \angle A = \angle B - \angle C. Is angle A acute? Statement I: \Delta ABC is not an obtuse-angled triangle. Statement II : Angle C is acute.

A Question is given followed by two Statements I and II. Consider the Question and the Statements. Which one of the following is correct in respect of the above Question and the Statements?

  1. A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
  2. B. The Question can be answered by using either Statement alone
  3. C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
  4. D. The Question can be answered even without using any of the Statements ✓

Correct Answer: D. The Question can be answered even without using any of the Statements

Explanation

From the given relation, \angle B = \angle A + \angle C. Since angles sum to 180^\circ, 2\angle B = 180^\circ, meaning \angle B = 90^\circ. Therefore, \angle A + \angle C = 90^\circ, ensuring \angle A is acute. Neither statement is required.

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