Question

The sum of $4$ adjacent interior angles of a pentagon is ${440}^{\circ }$, calculate the value of the $5^{th}$ interior angle.

• A. ${100}^{\circ }$
• B. ${110}^{\circ }$
• C. ${140}^{\circ }$
• D. ${40}^{\circ }$

Answer 1

The correct option is A ${100}^{\circ }$

The sum of the $4$ adjacent angles of the pentagon is ${440}^{\circ }$.

The number of sides in a pentagon is $5$.

The sum of all the interior angles of a polygon is $(n-2)\times {180}^{\circ }$.

For a pentagon, $(5-2)\times {180}^{\circ }$

$=3\times {180}^{\circ }$

$={540}^{\circ }$

Therefore, the $5^{th}$ interior angle will be ${540}^{\circ }-{440}^{\circ }={100}^{\circ }$