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Home > GC > Chapter 4 > Lesson 4.2.4 > Problem 4-85

4-85.

Find the values of and in the diagram at right. State the relationships you used.  

Two decreasing parallel lines are cut by two transversals. At the intersection of the left parallel line & the top transversal, the interior right angle is, theta.  About the right parallel line & the top transversal, the exterior right angle is, 112 degrees.  About the left parallel line & the bottom transversal, the interior right angle is, 85 degrees.  About the right parallel line & the bottom transversal, the exterior right angle is, alpha.

There are several correct methods.

The value of can be found by using corresponding and supplementary angles.

The value of can be found using corresponding angles.

At the intersection of the left parallel line & the top transversal, the exterior right angle is, 118 degrees, also.

So theta is 68 degrees.

And alpha is 85 degrees.