Question

The sum of the interior angles of a regular polygon is 1800°. Find the number of sides of the polygon.

Answer 1

Answer:

12

Step-by-step explanation:

Let side be n

We know that

$\boxed{\sf Sum\;of\;interior\:angles=(n-2)180}$

$\\ \sf{:}\dashrightarrow (n-2)180=1800$

$\\ \sf{:}\dashrightarrow n-2=\dfrac{1800}{180}$

$\\ \sf{:}\dashrightarrow n-2=10$

$\\ \sf{:}\dashrightarrow n=10+2$

$\\ \sf{:}\dashrightarrow n=12$

Answer 2

Answer:

12

Step-by-step explanation:

formula = 180(n – 2), where n is the number of sides.

180 ( n − 2 ) = 1800

Dividing both sides by 180 ,

n − 2 = 10

Adding 2 on both sides ,

n =

Since it is a 12-sided polygon, it is called a dodecagon