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Home > CCG > Chapter 3 > Lesson 3.2.6 > Problem 3-108

3-108.

Use the relationships in the diagram at right to solve for and . Justify your solutions.  

Think of how the highlighted angles relate to each other, and how the angles of a triangle relate to each other.

A horizontal transversal cuts through 2 parallel lines. At the right parallel line & the transversal, the exterior lower angle is 43 & at the left parallel line & the transversal, the interior upper angle is, x. A triangle is formed from segments from the top, left parallel line, the transversal left of angle x, & a segment between them. The angle opposite the parallel segment is, y, & opposite the transversal segment is 61. Shaded are 43, opposite angle & last interior triangle.

A horizontal transversal cuts through 2 parallel lines. At the intersection of the right parallel line & the transversal, the exterior lower angle is 43 and at the left parallel line & the transversal, the interior upper angle is, x. A triangle is formed with a segment from the top, left parallel line, a segment of the transversal left of angle x, & a segment between the two. The angle opposite the parallel segment is, y, & opposite the transversal segment is 61.