Points $A,B,C$ are three consecutive vertices of a regular polygon. Each interior angle is four ti

Question

Points $A,B,C$ are three consecutive vertices of a regular polygon. Each interior angle is four times its exterior angle. A diagonal $AC$ is drawn. Point $G$ lies on $AC$, and $ABFG$ is a rhombus, as shown. Find $\angle ABC$. [2] Find $\angle BFG$, explaining why triangle $ABC$ is isosceles and giving reasons for your angle calculations. [4]

Accepted Answer

(a) $144^\circ$ (b) $18^\circ$

Polygons - Angles in Regular Polygons

Polygons - Angles in Regular Polygons

Solution:

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