Question

In the diagram A,B,C,D
Is a cyclic
quadrilateral CB and AB are produced to E
Angle ABC=2n
Angle CEF=5n
Find the value of n
And angle ADC

Answer 1

I’m missing how E and F are placed — could you upload the diagram or clarify which lines/segments are extended to meet at E and F? For example, say explicitly which three points are collinear (is E on the line AB, on BC, or the intersection of two extended sides?), and which rays form angle CEF (i.e. which points are C–E–F).

A useful fact you’ll probably need: in a cyclic quadrilateral ABCD opposite angles are supplementary, so ∠ADC = 180° − ∠ABC = 180° − 2n. Once I know where E and F are I can use the appropriate external/intercept theorems to find n and the numeric value of ∠ADC.