Question

∠1 and ∠2 are supplementary, and m∠2 = 90.

A) ∠1 = 90, ∠2 = 90
B) ∠1 = 90, ∠2 = 0
C) ∠1 = 45, ∠2 = 45
D) ∠1 = 180, ∠2 = 0

Answer 1

When two angles are supplementary, their measures add up to 180 degrees. Since angle 2 is given as 90 degrees, angle 1 must be 90 degrees as well to add up to 180. Thus, the correct answer is ∠1 = 90 and ∠2 = 90.

Step-by-step explanation:

The question asks us to determine the measure of ∠1 when we know that ∠1 and ∠2 are supplementary angles and that the measure of ∠2 is 90 degrees. Supplementary angles are two angles whose measures add up to 180 degrees. Since we are given that m∠2 = 90, we can find m∠1 by subtracting 90 from 180.

m∠1 = 180 - m∠2
m∠1 = 180 - 90
m∠1 = 90

Therefore, the correct answer is A) ∠1 = 90, ∠2 = 90