Question

The figure shows a regular pentagon and two regular hexagons put together. The measure of $\angle ABC$ is

• A. ${10}^{\circ }$
• B. ${12}^{\circ }$
• C. ${14}^{\circ }$
• D. ${16}^{\circ }$

Answer 1

The correct option is B

${12}^{\circ }$

For regular pentagon, n=5.

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

$={72}^{\circ }$

Now, $e+i={360}^{\circ }$ (Linear pair)

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

$\Rightarrow i={108}^{\circ }$

For regular hexagon, n=6.

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

Now, $e+i={180}^{\circ }$ (Linear pair)

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

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

Now, ${120}^{\circ }+{108}^{\circ }+{120}^{\circ }+\angle ABC={360}^{\circ }$...(Angles around a point)

${348}^{\circ }+\angle ABC={360}^{\circ }$

$\Rightarrow \angle ABC={360}^{\circ }-{348}^{\circ }$

$={12}^{\circ }$