Question

If ∠a and ∠b are complementary, ∠b and ∠c are supplementary, and m∠a = 64o, then what is the measure of ∠c

a) 64 ∘

b) 90 ∘

c) 116 ∘

d) 180 ∘

Answer 1

The measure of ∠c can be found by first determining that ∠b is 26 degrees because ∠a and ∠b are complementary. Then, since ∠b and ∠c are supplementary, ∠c is 154 degrees. This measure is not among the answer choices provided, indicating a potential error in the question or choices.

Step-by-step explanation:

If ∠a and ∠b are complementary, this means that the sum of their measures is 90 degrees. Given that m∠a = 64 degrees, we can find m∠b by subtracting m∠a from 90 degrees:

m∠b = 90 degrees - 64 degrees = 26 degrees.

Next, we know that ∠b and ∠c are supplementary, meaning their sum is 180 degrees. Therefore, we can find m∠c by subtracting m∠b from 180 degrees:

m∠c = 180 degrees - m∠b = 180 degrees - 26 degrees = 154 degrees.

However, none of the answer choices matches this calculation. It appears there is a mistake either in the question or the choices provided. The measure of ∠c is not listed among the choices given.