Question

A polygon has $n$ sides. Two of its angles are right angles and each of the remaining angles is 144 degrees. Find the value of $n$.

Answer 1

Use the formula that states that the sum of the angles of an $n$-sided polygon is given by

$S=(n-2){180}^0........\left(1\right)$

Since we are given that the two angles are right angles and each of the remaining angles is ${144}^0$, therefore, the sum is:

$S={90}^0+{90}^0+(n-2){144}^0.........\left(2\right)$

Therefore setting (2) equal to (1) we get

$(n-2){180}^0={90}^0+{90}^0+(n-2){144}^0\Rightarrow (n-2){180}^0-(n-2){144}^0={180}^0\Rightarrow (n-2)({180}^0-{144}^0)={180}^0\Rightarrow (n-2)\left({36}^0\right)={180}^0\Rightarrow n-2=\frac{180}{36}\Rightarrow n-2=5\Rightarrow n=5+2=7$

Hence, the polygon has $7$ sides.