Ajay S. answered • 04/12/21

ACT Mathematics Tutor

Hey! Let me help you with this problem:

We know that segment XZ is a line, and we also know that segment QY intersects that line.

The most important part of this problem boils down to the concept that angles on a straight line add to 180^{o}. Because QY is a segment that creates two different angles, these add up to 180^{o}. These angles are (10a + 2) and (5a-2), so we can make the equation:

(10a + 2)^{o} + (5a - 2)^{o} = 180^{o}

After combining like terms...

15a^{o} = 180^{o}, so **a = 12**^{o}

The problem asks for m<XYQ, so plug in a = 12^{o} into (10a + 2) to get **122**^{o}