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20 POINTS please I am seriously terrible at proofs ..


Quadrilateral OPQR is inscribed inside a circle as shown below. Write a proof showing that angles O and Q are supplementary.

20 POINTS please I am seriously terrible at proofs .. Quadrilateral OPQR is inscribed inside a circle as shown below. Write a proof showing that angles O and Q class=

Verified Answer :

As anoutline, angles O and Q are inscribed angles which are measured by one-half of its intercepted arc. 
angle O = 1/2 arc RQP
angle Q = 1/2 arc ROP

so arcs RQP and ROP together make up the entire circle which has 360 degrees.

so angles O and Q is 1/2 (360) = 180 degrees (supplementary angles).

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