Remember that angles that are adjacent and linear must add up to 180°. Using this, you can determine the measure of an unknown angle if you know the measurement of the other angle(s) on that line. Additionally, recall that vertical angles, a pair of angles on opposite sides of a shared vertex, are congruent. Another fact to remember is the Triangle Angle Sum Theorem, which states that the sum of the measures of the angles in a triangle is 180°. Using these facts, you can determine the measurements of various angles in a diagram involving parallel lines and two intersecting transversals.
Now that you know about corresponding angles, you’re going to have to apply it to a situation, something like this, on a homework or a quiz. What you have to do here is take what you know, what you’re given and find the missing angles.
So I always start with well I know I have 80 degrees, I know I have two parallel lines and I have two transversals, so 80 corresponds to x. Since they’re corresponding angles, x must be 80 degrees, so I’m going to erase x and I’m going to write 80 degrees and I can come over here where I’m writing my answer and I’m going to write that x is 80 degrees.
So now that we found x, we need to find y and we need to find z. Well I can use what I know about these 3 angles being on a line and that they have to add up to 180 degrees. 80 plus 40 is 120 which means y has to be 60 if they sum to 180 degrees, so 60 degrees for y and last we have angle z. Now there’s a couple of ways that you can find angle z and I’ll show you a way that you’ve probably not seen. 40 degrees is a vertical angle with this angle right here. Vertical angles are always congruent. 40 degrees is corresponding to z, so that means that z must be 40 degrees.
So I’m going to come over here and I’m going to write that z must be 40 degrees. The key to angle cases use what you know. You probably are going to use some vertical angles, maybe a linear sum conjuncture and you’ll solve it pretty quickly.