. Find m∠1 if ∠1 is complementary to ∠2, ∠2 is supplementary to ∠3, and m∠3 = 126.

Answer 1

DEFINITION: Two angles are complementary if and only if their measurements add to 90 degrees.

DEFINITION: Two angles are supplementary if and only if their measurements add to 180 degrees.

PROVIDED: Angle 2 and Angle 3 are supplementary.

PROVIDED: Angle 3 is 126 degrees.

PROVIDED: Angle 1 and Angle 2 are complementary.

2 and 3 are supplementary, therefore m2 + m3 = 180

m3 = 126

m2 + 126 = 180

m2 = 180 - 126 = 54 degrees

m2 = 54

1 and 2 are complementary, therefore m1 + m2 = 90

m2 = 54

m1 + 54 = 90

m1 = 90 - 54 = 36 degrees

Therefore, m1 = 36