Circle geo question (1 Viewer)

[Thatstudentm9]

How did I get this wrong I’m year 11 3u finished HSC 2u just for fun I’m doing 3u

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[fan96]

The theorem involving angles at the centre and circumference is only true when these angles are subtended by the same arc.

In this case, the angle at the circumference is subtended by the arc .

And the angle subtended by the same arc at the centre is the reflex angle at , which is what you have found instead (obviously, could not be the non-reflex angle).

The non-reflex angle you are looking for is then , and so .

This is easily verified:

is a cyclic quadrilateral.

(opposite angles of a cyclic quad. are supplementary).