Question

The angles of a pentagon are in the ratio $5:4:5:7:6$ ; find each angle of the pentagon.

Answer 1

Let us consider all the angle of pentagon as 5x,4x, 5x, 7x and 6x
The sum of the interior angle of polygon is (2n-4) $\times {90}^{\circ }$
The sum of the interior angle of pentagon can be calculated as,
$(2n-4)\times {90}^{\circ }=(2\times 5-4)\times {90}^{\circ }=6\times {90}^{\circ }\text{We get},={540}^{\circ }\text{The sum of interior angles of pentagon}={540}^{\circ }27x={540}^{\circ }x=\frac{{540}^{\circ }}{27}\text{We get},x={20}^{\circ }\text{Thus, each angle,}5x=5\times {20}^{\circ }={100}^{\circ }4x=4\times {20}^{\circ }={80}^{\circ }7x=7\times {20}^{\circ }={140}^{\circ }6x=6\times {20}^{\circ }={120}^{\circ }$
Therefore, all the angles of a pentagon are ${100}^{\circ },{80}^{\circ },{100}^{\circ },{140}^{\circ }$ and ${120}^{\circ }$