Question

The interior angle of a regulary polygon is120 move than exterior angle find:
A.the interior angle and exterior angle.
B.the number of side

Answer 1

Given:

• The interior angle of a regular polygon is 120 more than exterior angle

To Find:

❶The interior angle and exterior angle.

❷the number of sides

Solution:

➺ the sum of interior angle and exterior angle in a polygon is 180°

➷let the exterior angle be x and interior angle be x + 120

so let's frame an equation:

$: \longrightarrow \tt x + 120 + x = 180\degree \\ \\ \\ : \longrightarrow \tt 2x + 120 = 180 \degree\: \: \: \\ \\ \\ : \longrightarrow \tt 2x = 180 - 120\degree \: \: \: \: \\ \\ \\ : \longrightarrow \tt 2x = 60\degree\: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \\ \\ \\ : \longrightarrow \tt \: x = \frac{60}{2} \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \\ \\ \\ : \longrightarrow \tt \: x = 30\degree\: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \:$

$\blue{ \underline{ \boxed{ \pink{ \mathfrak{ \therefore exterior \: angle = 30\degree \: and \: interior \: angle = 150\degree} \star}}}}$

$\sf \underline \purple{now \: we \: have \: to \: find \: the \: number \: of \: sides : } \:$

$: \implies \sf \: no. \: of \: sides = \frac{360}{n} \\ \\ \\ : \implies \sf \sf \: no. \: of \: sides = \cancel \frac{360}{30} \\ \\ \\ : \implies \sf \: no. \: of \: sides = 12 \:$

$\sf \underline \pink{hence \: the \: polygon \: has \: 12 \: sides\bigstar }$

Answer 2

Given:

The interior angle of a regular polygon is 120 more than exterior angle

To Find:

1. The interior angle and exterior angle.

2. The number of sides

Solution:

☛ the sum of interior angle and exterior angle in a polygon is 180°

☛ let the exterior angle be x and interior angle be x + 120

So let's frame an equation:

$\begin{lgathered}: \longrightarrow \tt x + 120 + x = 180\degree \\ \\ \\ : \longrightarrow \tt 2x + 120 = 180 \degree\: \: \: \\ \\ \\ : \longrightarrow \tt 2x = 180 - 120\degree \: \: \: \: \\ \\ \\ : \longrightarrow \tt 2x = 60\degree\: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \\ \\ \\ : \longrightarrow \tt \: x = \frac{60}{2} \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \\ \\ \\ : \longrightarrow \tt \: x = 30\degree\: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \:\end{lgathered}$

$\blue{ \underline{ \boxed{ \pink{ \mathfrak{ \therefore exterior \: angle = 30\degree \: and \: interior \: angle = 150\degree} \star}}}}$

$\sf \underline \purple{now \: we \: have \: to \: find \: the \: number \: of \: sides : }$

$\begin{lgathered}: \implies \sf \: no. \: of \: sides = \frac{360}{n} \\ \\ \\ : \implies \sf \sf \: no. \: of \: sides = \cancel \frac{360}{30} \\ \\ \\ : \implies \sf \: no. \: of \: sides = 12 \:\end{lgathered}$

$\sf \underline \pink{hence \: the \: polygon \: has \: 12 \: sides.}$