Given one of the angles, we want to find the other angles
We use the diagram given to follow the answers;
angle 2 = 180 - angle 1
This is because they lie on a straight line and angles on a straight line are supplementary
angle 2 = 180 - 53 = 127
angle 3 = angle 1 = 53 (they are corresponding angles and corresponding angles are congruent)
angle 4 = angle 2 = 127 (corresponding angles)
angle 5 = angle 2 = 127 (they are vertically opposite angles and vertically opposite angles are equal)
angle 1 = angle 6 = 53 (corresponding angles)
angle 7 = angle 4 = 127 (vertically opposite angles)
angle 3 = angle 8 = 53 (vertically opposite angles)
angle 1 = angle 9 = 53 (corresponding angles)
angle 2 = angle 10 = 127 (corresponding angles)
angle 3 = angle 11 = 53 (corresponding angles)
angle 4 = angle 12 = 127 (corresponding angles)
angle 13 = angle 10 = 127(vertically opposite angles)
angle 9 = angle 14 = 53 (vertically opposite angles)
angle 12 = angle 15 = 127 (vertically opposite angles)
angle 11 = angle 16 = 53 (vertically opposite angles)