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The Sum of Interior Angles of a Pentagon

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  • 0:04 Steps to Finding the Sum
  • 1:06 The Solution to the Sum
  • 2:16 Using the Sum of…
  • 3:09 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Do you know how many sides a pentagon has? You'll learn this and why the interior angles of all types of pentagon always add up to the same value. You'll also learn a formula you can use for any shape you come across.

Steps to Finding the Sum

A pentagon is a two-dimensional five-sided polygon. You can have pentagons with sides that are all the same length or you can have pentagons with sides that are all different.

Regardless of the type of pentagon you have, to find the sum of its interior angles, follow these steps.

Step 1: Use the Formula for the Sum of Interior Angles

You're going to use the formula to find the sum of interior angles of any shape. Here it is:


sum of interior angles


In this formula, the n stands for the number of sides of your shape. For your pentagon, it's a 5.

Step 2: Plug in 5 for n

Since your pentagon has five sides, you will plug in 5 for the variable n in the equation we just looked at so we, therefore, get:


sum of interior angles


Step 3: Solve

Your final step is to solve your formula. The formula tells you to subtract 2 from the number of sides of your shape. For your pentagon, this leaves you with 3. Then you have to multiply by 180 degrees.


sum of interior angles


The Solution to the Sum

Your solution after multiplying the 3 with the 180 degrees is 540 degrees.


sum of interior angles


This is true for any pentagon you have. Regular pentagons where all the sides and angles are the same will have a sum of interior angles of 540 degrees. Weird-shaped pentagons where one side is super long will also have a sum of interior angles of 540 degrees.

Why is this? This is because you can make any pentagon with three triangles. Remember, the 3 angles of any triangle always add up to 180 degrees. So if you have three triangles making up your pentagon, then your angles will always add up to 540 degrees (3 * 180 degrees). No matter how you stretch your pentagon, you still have your three triangles.

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