Angle 1 is a supplement of angle 2, and m angle 1 is 123 degrees. Angle 2 is a complement of angle 3. Find m angle 3.

Answer 1

2 angles are supplementary if their measures sum up to 180.

2 angles are complementary if their measures sum up to 90.

Since angle 1 and angle 2 are supplementary:

m(angle 1) +m(angle 2)=180 { m(angle) = measure of an angle}

123+m(angle 2)=180

m(angle 2) = 180-123

m(angle 2) = 57.

Now, since angle 2 is a complement of angle 3,

m(angle 2) + m(angle 3) =90

57 + m(angle 3)= 90

Therefore m(angle 3)= 33