Question

The given figure shows a sqaure, a regular pentagon and a regular hexagon put together. The measure of $\angle BAC$ is

• A. ${22}^{\circ }$
• B. ${32}^{\circ }$
• C. ${42}^{\circ }$
• D. ${52}^{\circ }$

Answer 1

The correct option is C

${42}^{\circ }$

For square,

each angle $={90}^{\circ }$

For a regular pentagon

n=5

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

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

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

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

For a regular hexagon n=6

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

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

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

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

Now, ${108}^{\circ }+{120}^{\circ }+{90}^{\circ }+\angle BAC={360}^{\circ }$

$\Rightarrow {318}^{\circ }+\angle BAC={360}^{\circ }$

$\Rightarrow \angle BAC={360}^{\circ }-{318}^{\circ }={42}^{\circ }$