Question

Given that 

∠A≅∠B, Gavin conjectured that  ∠A and ∠B are complementary angles.


Which statement is a counterexample to Gavin 's conjecture?


m∠A=45° and m∠B=45°

m∠A=25° and m∠B=25°

m∠A=10°and m∠B=15°

m∠A=30°and m∠B=60°

Answer 1

1) ∠A≅∠B, means that the two angles are congruent, this is they have the same measure.

2) Two angles are complementary angles if they sum up 90°.

So, let's examine the four statements:


A) m∠A=45° and m∠B=45°

This is not a counterexample, because it is a particular case where the two angles are congruent and they add up 90°, which is the very point of Gavin.

B) m∠A=25° and m∠B=25°

This is, indeed, a counterexample, because both angles are congruent and they do not add up 90°, driving to conclude that the conjecture of Gavin is not valid.

C) m∠A=10°and m∠B=15°

It is not a counter example because the two angles are not congruent.

D) m∠A=30°and m∠B=60°

It is not a counterexample because the two angles are not congruent.