Question

find the numberf sides of a regular polygon if each of its interior angle is4​

Answer 1

Step-by-step explanation:

$Measure \: of \: interior \: \angle = \frac{4 \pi^{c} }{5} \\ \\ = \frac{4 \times 180 \degree}{5} = 4 \times 36 \degree = 144 \degree \\ \\Measure \: of \: exterior \: \angle = 180 \degree - 144 \degree \\ \\= 36\degree \\ no \: of \: sides \: in \: regular \: polygon \: \\\\= \frac{360 \degree}{Measure \: of \: exterior \: \angle} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\\\= \frac{360 \degree}{36 \degree} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\\\= 10 \\ thus \: the \: given \: polygon \: has \: 10 \: sides \\\\ hence \: it \: is \: \: a \huge \:DECAGON \:$