Learning Task 5 : In your answer sheet , prove the theorem , using the given below . if a quadrilateral is inscribed in a circle , then its opposite angles are supplementary." Given : Quadriateral ABCD is inscribed in OE
Prove : ∠ABC and ∠ABC are supplementary ∠DAB and ∠DCB are supplementary

the answer is a and d

i think it is d. hope this

place r′ so that qr′ is parallel to the tangent.

now we get that ∠r′py=∠pr′q, where y is on the tangent, on the opposite side of p from x.

also, because of the symmetry, ∠r′py=∠qpx.

finally, note that no matter where we place r, as long as it's on the correct arc, we have ∠prq=∠pr′q.

stringing all these equalities together, we end up with ∠prq=∠qpx.

this picture will show how its going to look like.

hope this by jack monhen