what kind of angle is complementary to an angle on one side, but supplementary on another?

Question

10. An angle exists that is complementary to angle g on one side. On the other side, the angle is supplementary to angle h. The sum of the three angles is 200°. What is the measure of this common angle? (Show your work.)

Answer 1

x= missing middle angle

x + g = 90   (complementary angles add up to 90 degrees)

x + h = 180  (supplementary angles add up to 180)

x + g + h =200

since the sum of the 3 angles is 200 and just two of them, x +h is 180, that makes the 3rd angle, g equal to 20

if g =20, then x = 70 and h=110