# What is the sum of the measures of the interior angles of a 25-sided polygon?

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Apr 12, 2017

#### Answer:

Sum of the measures of the interior angles of of a 25-sided polygon is ${4140}^{\circ}$

#### Explanation:

Sum of the measures of all the exterior angles of any polygon, irrespective of its number of sides is always ${360}^{\circ}$.

As the measure of each pair of exterior and interior angles of a polygon adds up to ${180}^{\circ}$,

Sum of the measures of all the exterior angles and all interior angles of a 25-sided polygon is

$25 \times {180}^{\circ} = {4500}^{\circ}$

Hence, sum of all the interior angles of of a 25-sided polygon is ${\left(4500 - 360\right)}^{\circ} = {4140}^{\circ}$

From the above information, we can see that for an $n$ sided polygon

Sum of interior angles = $\left(n - 2\right) \cdot {180}^{\circ}$

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