### Home > CC2 > Chapter 8 > Lesson 8.3.3 > Problem 8-90

8-90.

Find the value of each variable in the following figures. Do not use a protractor. Use the properties of angles to help you. Homework Help ✎

a.

b.

c.

d.

e.

f.

g.

h.

37° + *a* = 90°. Solve for *a*.

53°

These angles are supplementary.

180° − 85° = *b*

47° and *c* are vertical angles. What does that tell you about the measure of angle *c*?

Set up an equation relating 137° and *d*. 137° + *d* = 180°.

Subtract 137° from both sides.

137° + *d* = 180°

−137° −137°

*d* = 43°

43°

*e* and 15° are complementary angles, meaning their sum is 90°.

*f* and 153° are vertical angles, and *i* and 153° are supplementary.

*f* = 153°, *i* = 27°

115° + *g* = 180°. Refer to part (d) for the steps to solving this problem.

95° + *h* = 180°. Now solve for the value of *h*.

85°