Question

The angles of a convex pentagon are in the ratio $2:3:5:9:11$. Find the measure of each angle.

Answer 1

Ratio of the angle is $2:3:5:9:11$

Let the angle be $2x,3x,5x,9x$ and $11x$.

The polygon has five angles and therefore five sides.

Sum of angles $=\left(\right(2n–4)\times {90}^0)$

$=\left(\right(2\times 5)–4)\times {90}^0$

$=(10–4)\times {90}^0$

$=6\times {90}^0={540}^0$

Therefore, $2x+3x+5x+9x+11x={540}^0$

$30x=6\times {90}^0\Rightarrow 30x={540}^0\Rightarrow x=\frac{{540}^0}{30}={18}^0$

Thus, the angles are:

$2x=2\times {18}^0$

$={36}^0$

$3x=3\times {18}^0={54}^0$

$5x=5\times {18}^0={90}^0$

$9x=9\times {18}^0={162}^0$

$11x=11\times {18}^0={198}^0$

Hence, the measure of angles are ${36}^0$, ${54}^0$, ${90}^0$, ${162}^0$ and ${198}^0$.