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=10° and m∠B=15°

m∠A=25° and m∠B=25°

m∠A=30° and m∠B=60°

m∠A=45° and m∠B=45°

Answer 1

Given ∠A≅∠B which means A and B are congruent, so A and B should have same value.

and also given that A and B are complementary angles which mean ∠A+∠B=90°

Now to find counterexample to Gavin's statement, we should find two angles satisfying ∠A≅∠B and contradicting ∠A+∠B = 90°

Let us check given options:-

A) since A and B are not equal, it is contradicting the first statement itself.

B) Here ∠A=25 = ∠B , hence it is satisfying congruent condition.

Let us check they are complementary or not by adding them.

∠A+∠B = 25°+25° = 50° ≠90°

Which means it is an counter example to Gavin's statement which tells that two congruent angles need not be complementary.

C) since A and B are not equal, it is contradicting the first statement itself.

D) Here ∠A=45°=∠B, hence it is satisfying congruent condition.

And ∠A+∠B = 45°+45° = 90°

Hence this is not an counter example.