Question

Theorem: A triangle has at most one obtuse angle. Eduardo is proving the theorem above by contradiction. He began by assuming that in △ABC,∠A and ∠B are both obtuse. Which theorem will Eduardo use to reach a contradiction?

A. If two supplementary angles are equal, the angles each measure 90°
B. The sum of the measures of the angles of a triangle is 180°
C. If two angles of a triangle are equal, the sides opposite the angles are equal.
D. The largest angle in a triangle is opposite the largest side.

Answer 1

Eduardo will use the theorem stating that the sum of the measures of the angles of a triangle is 180° (option B) to show that a triangle cannot have more than one obtuse angle.

Step-by-step explanation:

Eduardo is proving the theorem that a triangle has at most one obtuse angle by contradiction. He begins by assuming that in △ABC, ∠A and ∠B are both obtuse. To reach a contradiction, Eduardo would use the theorem option B. The sum of the measures of the angles of a triangle is 180°. By assuming two obtuse angles, the sum of ∠A and ∠B alone would exceed 180°, not even accounting for the third angle, ∠C. This directly contradicts the well-established fact that the sum of all three angles in any triangle, regardless of its type, must be exactly 180°. Since this assumption violates this fundamental property of triangles, it must not be true, proving that a triangle cannot have more than one obtuse angle.