# What is the number of sides in a polygon whose sum of the interior angles is 1800?

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12
Nov 13, 2016

Number of sides in a polygon is $12$

#### Explanation:

Sum of all the exterior angles of any polygon is always ${360}^{o}$.

As sum of every pair of interior and exterior angle is ${180}^{o}$,

sum of all the interior and exterior angles of a polygon with $n$ sides, is ${180}^{o} \times n$.

As sum of interior angles of given polygon is ${1800}^{o}$ and sum of exterior angles is ${360}^{o}$. Sum of all the angles of given polygon is ${2160}^{o}$.

As such ${180}^{o} \times n = {2160}^{o}$ and $n = {2160}^{o} / {180}^{o} = 12$.

Hence, number of sides in a polygon is $12$

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2
May 17, 2018

$12$ sides

#### Explanation:

All polygons can be divided up into triangles by joining one vertex to all of the other vertices.

The number of triangles is always two less than the number of sides.

If you know the number of triangles you add $2$ to find the number of sides.

Every triangle has 180°

Number of triangles: $\frac{1800}{180} = 10$ triangles

Number of sides: $10 + 2 = 12$ sides

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