Four-sided Figures: Finding Unknown Angles - Part 1

Example:

In the figure below, find the unknown marked angles.


Since there are two pairs of parallel sides in the above figure, WXYZ is a parallelogram.

Therefore,
∠y = ∠w = 53°

The sum of a pair of angles between two parallel lines is 180°.
Also,
∠y + ∠z = 180°
∠z = 180° - 53 ° = 127°

The opposite angles of a parallelogram are equal.
And,
∠x = ∠z = 127°