### Home > CCG > Chapter 5 > Lesson 5.2.1 > Problem 5-53

5-53.

Use the relationships found in each of the diagrams below to solve for and

*. Assume the diagrams are not drawn to scale. State which geometric relationships you used.*

Solve for the missing angle in the triangle with

and . Use the Triangle Angle Sum Theorem to solve for the missing angle. and theangle are supplementar *y*angles, because they form a linear pair.The

angle and the angle across from it are vertical angles and vertical angles are congruent. Using the Triangle Angle Sum Theorem and the triangle on the right,

so

,

Find the measures of any angles that may relate to the unknown angles by using the angles given.

This is a special right triangle. Try drawing it to scale and then solve for

and .