Prove that any outer angle of a cyclic quadrilateral is equal to the inner angle at the opposite vertex.

Prove that any outer. angle of a cyclic quadrilateral is equal to the interior angle, at the opposite vertex.

Prove that in any triangle, the outer angle at a vertex is equal to the sum of the inner arigles at the outer two vertices.

The sum of the outer angles of a polygon is twice the sum of the inner angles. How many sides does it have? What if the sum of outer angles is half the sum of inner angles? And if the sums are equal?

Draw a quadrilateral and mark any two outer angles. Is thére any relation between the sum of these two and the inner angles at the other two vertices?

Prove that the lengths of the perpendiculars from any point on the bisector of an angle to the sides are equal.

Prove that if both pairs of opposite sides of a quadrilateral are equal, then it is a parallelogram.