Question

Determine whether the following conjecture is true or false. Give a counterexample if the answer is false. ∠A and ∠B are supplementary, ∠B and ∠C are complementary, then ∠A and ∠C are complementary angles.

Answer 1

The conjecture is false.

Explanation:

Let m∠B = 60°. 

Since ∠B and ∠A are supplementary, they add to 180, this means that
m∠A = 180-60 = 120°.

Since ∠B and ∠C are complementary, they add to 90, this means that
∠C = 90-60 = 30°.

If ∠A and ∠C are complementary, then they add to 90°:

120+30=150

This is not true.