How do you find angles of a parallelogram?

To find the angles of a parallelogram, you have to know at least one angle (although it could be an interior or an exterior angle). There are several facts about all parallelograms:

  1. the sum of the interior angles is 360˚ (true for all quadrilaterals)
  2. opposite angles are congruent (angles that are diagonal in parallelograms have the same measure)
  3. consecutive angles are supplementary (angles that are connected by a single side add up to 180˚)

If you know any of the interior angles, you can use a combination of the above rules to find the rest. If all you know is an exterior angle, then use the fact that an interior angle and its exterior angle are supplementary (because they are a linear pair--they make a line) to find the measure of the interior angle; then use the rules given above.