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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

$120+x=180$

$-120\quad -120$

$x=60^{\circ}$

<- parallel lines cut by transversal
$80+x=180$
$-80 \quad -80$
$x=100^{\circ}$