Question

The figure shows a regular heptagon and a regular hexagon are put together. Then the measures of $\angle ABC$ is

• A. ${112}^{\circ }$
• B. ${114}^{\circ }$
• C. ${122}^{\circ }$
• D. ${121}^{\circ }$

Answer 1

The correct option is A

${112}^{\circ }$

For regular hexagon, n=6.

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

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

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

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

For a regular heptagon, n=7.

$\Rightarrow$ Each exterior angle $=\frac{360}{7}$

$={52}^{\circ }$

Now, $e+i={180}^{\circ }$

$\Rightarrow 52+i={180}^{\circ }$

$\Rightarrow i={180}^{\circ }-{52}^{\circ }$

$i={128}^{\circ }$

Now, ${128}^{\circ }+{120}^{\circ }+\angle ABC={360}^{\circ }$

$\Rightarrow {248}^{\circ }+\angle ABC={360}^{\circ }$

$\Rightarrow \angle ABC={360}^{\circ }-{248}^{\circ }$

$\therefore \angle ABC={112}^{\circ }$