Points $A,B,C$ are three consecutive vertices of a regular polygon. The ratio of each interior ang

Question

Points $A,B,C$ are three consecutive vertices of a regular polygon. The ratio of each interior angle to each exterior angle is $7:1$. Side $AB$ is extended beyond $B$ to $G$, where $BC=CG$. A rhombus $BCGH$ is formed, with $H$ on the opposite side of $BG$ from $C$. Find $\angle CBG$. [2] Find $\angle CGH$, showing how you use triangle $BCG$ and the properties of a rhombus. [4]

Accepted Answer

(a) $22.5^\circ$ (b) $45^\circ$

Polygons - Angles in Regular Polygons

Polygons - Angles in Regular Polygons

Solution:

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