Question

HELP PLEASE

Prove that opposite angles of an inscribed shape are supplementary, (equaling to 180 degrees).
In other words, if a quadrilateral was inscribed in a circle, prove how the opposite angles are equal to 180 degrees.
NOTE: you cannot say "because of the inscribed angles conjecture."

Answer 1

A good way of understanding why opposite angles in an inscribed shape are supplementary is by splitting up the shape itself. For example, if you had a quadrilateral inscribed within a circle, you could "cut" up the shape by the diagonal into two triangles. If you put the opposite angles next to each other (by lining up the triangles), you would notice a straight line. This line would prove that the opposite angles are equal to 180 degrees.