Extend all the sides of the quadrilateral (if not already done) with the pencil. Extend the sides to create exterior angles, which can help you solve all the angles of a quadrilateral. Redraw the quadrilateral on a piece of scratch paper if you cannot draw in your book or worksheet.
Examine the angles that are given. Note that the sum of angles on a straight line always equals 180 degrees. For example, if you are given an interior angle of 60 degrees, the exterior angle on the same line has to be 120 degrees. Use a calculator to check your work, if needed.
Look for any congruent angles in the quadrilateral. Congruent angles are angles that have the same measurement. Look for given angles that are mirror images of other angles. For example, you may be given an interior angle of 80 degrees that is congruent to an exterior angle. That exterior angle will also measure 80 degrees.
Note that the sum of all the interior angles of a quadrilateral is 360 degrees. Solve for all unknown angles using this principle after solving for congruent angles and straight lines.
Add all the interior angles together and subtract them from 360 to find any one missing interior angle.