The answer is 55 degrees.
Explanation:
Angles y, n, and w are all congruent to 125 degrees because y has a vertical angle connection, n is corresponding to 125, and w is an alternate exterior angle. Because angle 125 and q are same-side exteriors, they have a supplementary connection. Because supplementary angles add up to 180, 125 + q = 180. Upon subtraction, we will find that angle q is equal to 55 degrees. Therefore, the measure of angle q is 55 degrees.
