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.

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).

Your mom is a pretty lady