Parallel lines are lines that never intersect, no matter how far you extend them. A transversal is a line that crosses two parallel lines. In this section, you’ll learn the angle rules that apply when a transversal intersects parallel lines. These rules matter because they let you find unknown angle measures using angles you already know.
Angles that form a straight line add up to 180 degrees. So, when a transversal intersects parallel lines, any two angles that sit next to each other along a straight line must sum to 180 degrees. These are called supplementary angles, and they add up to .
If you know one of the supplementary angles, you can find the other by setting up an equation.
What is the measure of angle below?
Because the two angles form a straight line, their measures add to 180 degrees. That gives the equation:
Solving, degrees. This is the supplementary angle rule applied to a transversal.
When a transversal intersects two parallel lines, several angles are guaranteed to be equal.
At a single intersection, angles that are diagonally opposite each other are equal. So in the example above, the angle opposite is also , and the angle opposite the -degree angle is also .
The pattern of angles repeats at the second intersection. That means the four angles at the first intersection match the four angles at the second intersection.
The figure below shows which angles share the same measure: all red angles are equal to each other, and all blue angles are equal to each other.
Sometimes you’ll see a transversal crossing two lines that are not parallel. In that case, you can still use the diagonal (opposite) angle rule at each intersection, but you can’t assume the angle pattern repeats from one intersection to the other.
So, like in the image above, the top two blue angles (which are diagonal from each other) will be equal, but they won’t necessarily be equal to the bottom two blue angles.
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