Question

Given that ∠A≅∠B , Evelia conjectured that ∠A and ∠B are acute angles. Which statement is a counterexample to Evelia's conjecture?

(high school)
m∠A=114° and m∠B=170°

m∠A=126° and m∠B=126°

m∠A=30° and m∠B=40°

m∠A=45° and m∠B=45°

Answer 1

B

Explanation:

Given that ∠A ≅ ∠B, Evelia conjectured that ∠A and ∠B are acute angles.

Consider all options:

A. If m∠A=114° and m∠B=170°, then angles A and B are not congruent, so this is not a counterexample.

B. If m∠A=126° and m∠B=126°, then angles A and B are congruent and both these angles are obtuse (their measures are greater than 90°). This means that two obtuse angles can be congruent, so this is a counterexample. True option.

C. If m∠A=30° and m∠B=40°, then angles A and B are not congruent, so this is not a counterexample.

D. If m∠A=45° and m∠B=45°, then angles A and B are congruent, so this examples show two congruent acute angles. But if we have to prove some statement, we have to prove this statement for an arbitrary angles, not for one pair of angles. Moreover, this is an example illustrating given statement, but is not a counterexample.