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

This conjecture is false, A and C don't have to be complementary angles.

Let Angle A be 100 and Angle B be 80 degrees. They are supplementary (sum of 180).
Let Angle C be 100 and Angle B is still 80 degrees. They are supplementary.

However, Angle A and Angle C are not complementary (sum of 90).