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Home > CCG > Chapter 2 > Lesson 2.1.5 > Problem 2-55

2-55.

Solve for in the diagram at right.  

Two transversal lines cut two parallel lines. About the point of intersection of the top parallel line and the left transversal line are angles starting at top left going clockwise and labeled as follows: blank, blank, blank, and blank. About the point of intersection of the top parallel line and the right transversal line are angles starting at top left going clockwise and labeled as follows: blank, 15 x minus 30 degrees, blank, and blank. About the point of intersection of the bottom parallel line and the left transversal line are angles starting at the top left going clockwise and labeled as follows: blank, blank, blank, and 10 x + 5 degrees. About the point of intersection of the bottom parallel line and the right transversal line are angles starting at the top left going clockwise and labeled as follows: blank, blank, blank, and blank. Solve for x.

What is the relationship between angles and ?

The angle is congruent to angle .

Since angles and are corresponding angles on two parallel lines intersected by a transversal, they are also congruent.

The same rule applies to angle and the angle valued , so they are also congruent.

About the point of intersection of the bottom parallel line and the left transversal line are angles starting at the top left going clockwise and labeled as follows: blank, z, blank, and 10 x + 5 degrees.

About the point of intersection of the bottom parallel line and the left transversal line are angles starting at the top left going clockwise and labeled as follows: blank, z, blank, and 10 x + 5 degrees. About the point of intersection of the bottom parallel line and the right transversal line are angles starting at the top left going clockwise and labeled as follows: blank, y, blank, and blank.

Since , and , what can we conclude? Use your conclusion to solve for .