We know that alternate interior angles are congruent and same-side interior angles are supplementary, this will help us with solving this problem.
x = 105°
105° + 75° = 180°
Because we have the 75° already labeled, we can fill in the other 75°, since they are corresponding angles. Then we can see that it will be 105° next to the bottom 75°, since they are equal to the straight line, which means together they will be 180°.
y = 75°
105° + 75° = 180°
Using the same thing as we used for x, y would be 75° because of vertical angles, along with the same-side interior angle theorem.
w = 94°
94° + 86° = 180°
Since we already had the 86° labeled, we can automatically fill it in on top because of the corresponding angles theorem. We can put 94° next to the bottom 86°, because they are supplementary and equal 180°. Then we can either use the corresponding angles theorem to find w, or we can fill in vertical angles for 94°, then fill in w because alternate interior angles are congruent.
z = 86°
94° + 86° = 180°
Since we already have the 86° labeled for us, we can find z using vertical angles.
