Finding the Measure of an Angle Given Parallel Lines

Example: In the diagram below, the lines k and l are parallel. What is the measure of angle x?

Since we know that lines k and l are parallel, we know that 117 and y are supplementary angles, meaning they add to equal 180. From there, we can calculate the value of y to be…

117 + y = 180           so y = 63 degrees

Angle x and y must be equal since k and l are parallel with a single line transecting them. So we know that x is 63 degrees

Example: Find the measure of x.

when parallel lines are cut by a transversal, corresponding angles are congruent.

We know that


-120\quad -120


<- parallel lines cut by transversal
-80 \quad -80