### Home > GC > Chapter 5 > Lesson 5.2.1 > Problem 5-47

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

*x*and*y*. Assume the diagrams are not drawn to scale. State which geometric relationships you used. Homework Help ✎

Solve for the missing angle in the triangle with 70° and 41°. Use the triangle sum theorem to solve for the missing angle.

41° + 70° + missing angle = 180°

missing angle = 69°

*y* and the 69° angle are supplementar*y* angles, because they are a linear pair

69° + *y* = 180°

*y* = 111°

The 69° angle and the angle across from it are vertical and vertical angles are congruent.

Using the triangle sum theorem and the triangle on the right,

69° + 58° + *x* = 180° so *x* = 122°

*y* = 79°, *x* = 47°

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 *x* and *y*.