Question

Aach interior angel of a regular polygan is 156° .Find the number of sides of the polygan.

a) 10°
b) 15°
c) 20°
d) 30°

Which option is correct ?​

Answer 1

I think it’s 10 pls click thx under it pls

Answer 2

Correct Question :-

• Each interior angle of regular polygon is 156°. Find the number of sides of the polygon.

Answer :

• $\large{\bf{b)~15°}}$ Option is correct.

Given :-

• Interior angle of a regular polygon is 156°.

To find :-

• Find the each angle of sides ?

$\large\dag$ Formula Used :

• $\large\boxed{\bf{\frac{(n \: - \: 2) \: \times \: 180}{n} }}$$\huge\purple\star$

Solution :-

:$\implies$ 360n + 180 = 156

$~~~~~$:$\implies$ 360n = 180 - 156

$~~~~~~~~~~$:$\implies$ 360n = 24

$~~~~~~~~~~~~~~~$:$\implies$ n = $\large{\sf{ \frac{360}{24} }}$

$~~~~~~~~~~~~~~~~~~~~$:$\implies$ n = ${\sf{\dfrac{\cancel{360}}{\cancel{24}}}}$

$~~~~~~~~~~~~~~~~~~~~~~~~~$:$\implies$ $\large{\underline{\boxed{\pink{\bf{Side~=~15°}}}}}$★

$\large\dag$ Hence,

• The each angle of sides = ${\bf{15°}}$ $\large{\bf\green{✓}}$