Question

prove that the sum of the (interior) angles of a pentagon is 540

Answer 1

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.

The Steps

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 of any pentagon, follow these steps.

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

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





In this formula, the n stands for the number of sides of your shape. For your pentagon, it is 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 above equation.





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 are to multiply by 180 degrees.





The Solution

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





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.

Answer 2

Given:

A pentagon

To prove:

The sum of interior angles is 540°

Solution:

We know that the total number of sides of a pentagon=5

The sum of its interior angles can be calculated by multiplying 180° by the number of sides minus 2.

So, the number of sides, n=5

The required sum of the interior angles=(n-2)×180°

Using values,

=(5-2)×180°

=3×180°

=540°

Hence, it is proved.