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

Then teach the underlying concepts
Don't copy without citing sources
preview
?

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

18
Apr 12, 2017

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

• 13 minutes ago
• 17 minutes ago
• 23 minutes ago
• 33 minutes ago
• 55 seconds ago
• 8 minutes ago
• 8 minutes ago
• 9 minutes ago
• 9 minutes ago
• 10 minutes ago
• 13 minutes ago
• 17 minutes ago
• 23 minutes ago
• 33 minutes ago