### Home > GC > Chapter 6 > Lesson 6.2.5 > Problem 6-85

6-85.

For each shape below, use the geometric relationships to solve for the given variable(s). Show all work. Name the geometric relationships you used. Homework Help ✎

What is the sum of the angles within a triangle?

*x* = 15°, Triangle Angle Sum

What do the tick marks on the sides of the triangles mean?

*k* = 5, Isosceles triangle

Extend the parallel sides.

Parallel lines have same side interior supplementary angles.

*w* + (4*t* + 13) = 180°*w* + (8*t* − 23) = 180°

By the Equal Values Method: *w* + (8*t* − 23) = *w* + (4*t* + 13)

*w* + 8(9) − 23 = 180*w* + 72 − 23 = 180*w* + 49 = 180*w* = 131°

4*t* = 36*t* = 9°

Parallel lines

Use the Law of Cosines to solve for the unknown side.