ABCD isacyclicquad.AB,DC extendsatE.DA,CB extendsatF.angles AFB=30,BEC=20,findallanglesof quad

Question

IGCSE math, circle geometry problem

Answer 1

The opposite angles of a cyclic quadrilateral are supplementary, that is, their sum is 180°.

In the quadrilateral ABCD, ∠C=180-A, ∠D=180-B.

In triangle FCD: 30+180-A+180-B=180 (sum of angles F, C and D), so A+B=210°.

In triangle EBC: 20+B+180-A=180 (sum of angles E, B and C), A-B=20°.

Add these two equations together: 2A=230, A=115° and B=A-20=95°.

So the angles are: A=115°, B=95°, C=65°, D=85°.