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.
