How to work out the sum of interior angles of a polygon in 2 easy steps (heptagon and decagon examples)

The total of all the inside angles of a polygon is known as the sum of interior angles. To work out the sum of interior angles for a polygon follow these two simple steps:

Step 1: Pick a corner and draw all the diagonals from this corner (a diagonal is a line that joins one corner of a polygon to another corner).

Step 2: Multiply the amount of triangles that you have made by 180⁰ (since the angles in the triangle add up to 180⁰ and these form the interior angles of your polygon).

Alternatively, you can use the following formula to work out the sum of interior angles:

Sum of interior angles = 180(n-2)

(n is the amount of sides that the polygon contains).

Example 1

Work out the sum of interior angles of this heptagon (7 sides).

To begin with pick any corner of the heptagon and make all the diagonals from this corner.

You should have drawn 4 diagonals which makes a total of 5 triangles.

All you have to do now is multiply the amount of triangles by 180:

5 × 180 = 900⁰.

So the sum of interior angles of a heptagon is 180⁰.

If you prefer using the formula to work out the sum of interior angles all you need to do is substitute n= 7 into the formula as the polygon has 7 sides:

Sum of interior angles = 180(n-2)

Sum of interior angles = 180 × (7-2)

Sum of interior angles = 180 × 5

Sum of interior angles = 900⁰.

Example 2

Work out the sum of interior angles of this decagon (8 sides).

Just like the first example, begin with picking any corner of the decagon and make all the diagonals from this corner.

You should have drawn 7 diagonals which makes a total of 8 triangles.

All you have to do now is multiply the amount of triangles by 180:

8 × 180 = 1440⁰.

So the sum of interior angles of a decagon is 180⁰.

If you prefer using the formula to work out the sum of interior angles all you need to do is substitute n= 10 into the formula as the polygon has 10 sides:

Sum of interior angles = 180(n-2)

Sum of interior angles = 180 × (10-2)

Sum of interior angles = 180 × 8

Sum of interior angles = 1440⁰

So the sum of interior angles of a decagon is 1440⁰.

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2 comments

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jean0 4 years ago

more examples !


jean0 profile image

jean0 4 years ago

i can't understand .. who could help me about the"Sum of interior angle"

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