What is m∠XYQ? A line segment QY intersects another line segment XZ at the point Y to form the angles XYQ and QYZ measuring (10a+2) degrees and (5a-2) degrees respectively. m∠XYQ =

Question

Answer 1

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