why inscribed quadrilaterals have opposite angles that are supplementary?

Answer 1

an angle inscribed in a circle is equal to half of the intercepted arc

the opposite angles of a quadrilateral intercept the entire circle
... 1/2 * 360 = 180

Answer 2

@Scott, I want a answer in 5-6 lines. How can I make this answer big?

Answer 3

Again, see:
http://www.jiskha.com/display.cgi?id=1496883964