By extending the sets of parallel lines, you can see that the angles marked on this diagram are all the same size (alternate angles, corresponding angles and/or vertically opposite angles).

Angles are equal if they are vertically opposite angles, or corresponding or alternate angles in parallel lines.
There are 10 angles the same size as the orange angle.
You can see from the picture below that two of the angles plus a right angle form a revolution (360 degrees).

If the angle is Y degrees,
2 x Y + 90 = 360
2 x Y = 360 - 90
2 x Y = 270
Y = 135
Each of the marked angles is 135 degrees.