Question

30 POINTS

Each interior angle of a polygon is 150 degrees. Find the number of sides.

An explanation is needed.

Answer 1

$\huge\bf\underline{\red{A}\purple{n}\pink{s}\orange{w}\blue{e}\green{r}}$

= 180° - 150°

= 30°

It's Adjacent agle = 30°

No. of sides = 360/30

= 12

So, no. of sides = 12.

❥ HoPe this helps!!

Answer 2

Given :

• Each interior angle of a polygon = 150°

To find :

• Number of sides of the polygon

Knowledge required :-

• Interior angle + Exterior angle = 180°

• Number sides of the polygon = $\boldsymbol{ \dfrac{360 ^{ \circ}}{\sf exterior \: \: angle}}$

~Understanding the concept ::

Here, we are given each interior angle of the polygon. So, firstly we will find the each exterior angle of the polygon. Then we will substitute the value of the exterior angle of the polygon in the formula of number of sides to find its value.

Solution :

$\underline{\gray{\pmb{Interior ~~angle ~ + ~ Exterior ~~angle ~=~180^{\circ}}}}$

⠀⠀⠀⇒ 150° + Exterior angle = 180°

⠀⠀⠀⇒ Exterior angle = 180° - 150°

⠀⠀⠀⇒ Exterior angle = 30°

$\underline{\pmb{Exterior~~angle = 30^{\circ}}}$

Number of sides = $\boldsymbol{ \dfrac{360 ^{ \circ}}{\sf exterior \: \: angle}}$

⠀⠀⠀⇒ No. of sides = $\boldsymbol{ \dfrac{360 ^{ \circ}}{\sf 30^{\circ}}}$

⠀⠀⠀⇒ No. of sides = $\boldsymbol{ \dfrac{36\not0 ^{ \circ}}{\sf 3\not0^{\circ}}}$

⠀⠀⠀⇒ No. of sides = $\boldsymbol{ \dfrac{36}{\sf 3}}$

⠀⠀⠀⇒ No. of sides = 12

$\underline{\pmb{No.~of~sides~of~the~polygon~=~12}}$

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Know More :-

• Sum of interior angles of a polygon = (2n - 4) × 90

A regular polygon has :-

• All its sides equal to each other.
• All its interior angles equal to each other.
• All its exterior angles equal to each other.