Question

In the following diagram,

ℓ
∥
m
.



Solve for each of the variables w, x, y, and z. For each solution, explain, in complete sentences which special angles allowed you to create an equation in order to find a solution.

Answer 1

w = 94 degrees

x = 105 degrees

y = 75 degrees

z = 86 degrees

Explanation:

The 75 degree angle + x = 180 degrees, because together they form straight line. They are supplementary angles.

180 - x = 75

x = 105 degrees

The 86 degree angle and z are equal, because they are vertical angles...they share a vertex. So z = 86 degrees

In some of the other problems we've looked at together, we've talked about corresponding angles. Angles in the same position on the next parallel line, cut by a transversal. The angle right above x, where p intersects l, corresponds to y. I've called it Y' in the picture I'm attaching.

So if the 75 degree angle is equal to its vertical angle, Y', which is equal to its corresponding angle of y. y = 75 degrees

Using all of what's here about supplementary angles and corresponding angles, you know that the two angles in the z/86 degree area are 94 degrees. (180 - 86 = 94) Which means w and its vertical angle are also 94 degrees. w = 94 degrees.

I'm sorry this is so wordy. I don't want it to be confusing for you. I am hoping I can help you understand enough so these problems don't stress you out :) I have circled vertical angle pairs (about half of them) in pink. I have circled the supplemental angle pairs (about half of them) in purple.