Question

The figure shows a regular pentagon and a regular hexagon put together. The measure of $\angle PQR$ is

• A. ${122}^{\circ }$
• B. ${132}^{\circ }$
• C. ${142}^{\circ }$
• D. ${152}^{\circ }$

Answer 1

The correct option is B

${132}^{\circ }$

For a regular hexagon, n=6.

Each exterior angle $=\frac{360}{6}={60}^{\circ }$

$\therefore i+{60}^{\circ }={180}^{\circ }$

$\Rightarrow i={180}^{\circ }-{60}^{\circ }$

$\Rightarrow i={120}^{\circ }$

For a regular pentagon, n=5

Each exterior angle $=\frac{360}{5}={72}^{\circ }$

$\therefore i+e={180}^{\circ }$

$\Rightarrow i+{72}^{\circ }={180}^{\circ }$

$\Rightarrow i={180}^{\circ }-{72}^{\circ }={108}^{\circ }$

$\therefore$ Angle about a point is ${360}^{\circ }$

$\therefore {120}^{\circ }+{108}^{\circ }+\angle PQR={360}^{\circ }$

$\Rightarrow \angle PQR={360}^{\circ }-{228}^{\circ }$

$\Rightarrow \angle PQR={132}^{\circ }$