Question

In a regular pentagon the ratio of interior angle : exterior angle = ___

• A. 2 : 3
• B. 1 : 3
• C. 3 : 2
• D. 3 : 1

Answer 1

The correct option is C

3 : 2

A pentagon has 5 sides. Since the pentagon is regular, all its angles and sides are equal.

Let the interior angle be $x^{\circ }$ and exterior angle be $y^{\circ }$.

$\because$ sum of exterior angles in a polygon is ${360}^{\circ }$

$\Rightarrow 5y^{\circ }$ = ${360}^{\circ }$

$\Rightarrow y^{\circ }=\frac{360}{5}={72}^{\circ }$

$\because$ sum of exterior angle and its respective interior angle in a polygon is ${180}^{\circ }$

$\Rightarrow x+y={180}^{\circ }$

$\Rightarrow x={180}^{\circ }-y^{\circ }$

$={180}^{\circ }-72\circ$

$={108}^{\circ }$

Now, $\frac{interiorangle}{exteriorangle}=\frac{x}{y}=\frac{108}{72}=\frac{3}{2}$

Hence, interior angle : exterior angle = 3 : 2