Is angle A in the triangle larger than 90 degrees? Statement A: The sum of…

CONCEPT: This is a data-sufficiency question — a statement is sufficient if the information it gives allows a definite yes-or-no answer to the question, whatever that answer turns out to be; it does not need to confirm “yes”. The geometry fact used here is the angle-sum property of a triangle: the three interior angles of any triangle always add up to 180°.

1. Test Statement A alone: it gives B + C = 140°. By the angle-sum property, A = 180° − (B + C) = 180° − 140° = 40°.

2. Since 40° is a single, fixed value and it is not greater than 90°, Statement A alone gives a definite “No” — so it is sufficient by itself.

3. Test Statement B alone: it gives B = 60°, so A + C = 180° − 60° = 120°. The split between A and C is not fixed by this alone.

4. Because C can range anywhere between 0° and 120°, A can take any value in that same range too — sometimes above 90° (e.g. A = 100°, C = 20°) and sometimes below (e.g. A = 40°, C = 80°). Statement B alone cannot give a definite answer.

CROSS-CHECK: Plugging A = 40° back in confirms B + C = 140°, consistent with Statement A. Once Statement A alone settles the question, there is no need to also invoke Statement B — which rules out requiring both statements or claiming either one works alone.

Therefore, Statement A alone is sufficient to determine that angle A is not greater than 90°.