In the figure below, $XABCY$ is part of a regular polygon, $ABGFED$ is a regular hexagon and \(B

Question

In the figure below, $XABCY$ is part of a regular polygon, $ABGFED$ is a regular hexagon and $BCHG$ is a square, where $AB, BC$ and $BG$ are common sides. Find the sizes of angle $ABG$, angle $ABC$, angle $DAX$, angle $HCY$. Hence find the number of sides and the sum of exterior angles of the polygon, respectively.

Accepted Answer

(a) $\angle ABG=120^\circ$ (b) $\angle ABC=150^\circ$ (c) $\angle DAX=90^\circ$ (d) $\angle HCY=120^\circ$ (e) $12$ sides, exterior-angle sum $=360^\circ$

Polygons

Polygons

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