SOLUTION: a cyclic quadrilateral is noted as ABCD. Prove that (m< a) + (m< c) = (m< b) + (m< d)

Question 475853: a cyclic quadrilateral is noted as ABCD. Prove that (m< a) + (m< c) = (m< b) + (m< d)

Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Assuming that a is the angle opposite vertex A, the proof is quite straightforward. The arc intercepted by angle a and the arc intercepted by angle c do not intersect, and they add up to the whole circle (360 degrees). This means that angle a + angle c = 180 degrees (since the angle with vertex on the circle is half of the degree measure of the arc). Similarly, angle b + angle d = 180 degrees, so we are done.
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