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Interior Angle Sums

In this worksheet, students calculate the sum of the interior angles of the given polygons.

'Interior Angle Sums' worksheet

Key stage:  KS 3

Curriculum topic:  Geometry and Measures

Curriculum subtopic:  Derive/Use the Sum of Angles for Deduction

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

 You already know that the interior angles of a triangle add up to 180º.

 

Polygons with more sides have a larger sum of interior angles.

To work out the sum of the interior angles of a polygon with more sides, we choose one of the corners and split the polygon into triangles.  Each triangle will contain 180º.

 

Example

Work out the sum of the interior angles of this hexagon.

 

 

Answer

Choose any one corner.

 

 

Draw diagonals from the chosen corner to form triangles.

 

 

There are 4 triangles inside the hexagon.

4 x 180º = 720º

 

The sum of the interior angles of a hexagon is 720º.

Work out the sum of the interior angles of this rectangle in degrees.

(just write the number)

 

Work out the sum of the interior angles of this heptagon in degrees.

(just write the number)

 

Work out the sum of the interior angles of this pentagon in degrees.

(just write the number)

 

Work out the sum of the interior angles of this irregular pentagon in degrees.

(just write the number)

 

Work out the sum of the interior angles of this octagon in degrees.

(just write the number)

 

What is the sum of the interior angles of any quadrilateral?

(just write the number)

 

 

What is the sum of the interior angles of any nonagon (9 sides)?

(just write the number)

 

 

What is the sum of the interior angles of any decagon ?

(just write the number)

 

 

What is the sum of the interior angles of any 12-sided polygon ?

(just write the number)

 

 

What is the sum of the interior angles of any 11-sided polygon ?

(just write the number)

 

 

  • Question 1

Work out the sum of the interior angles of this rectangle in degrees.

(just write the number)

 

CORRECT ANSWER
360
  • Question 2

Work out the sum of the interior angles of this heptagon in degrees.

(just write the number)

 

CORRECT ANSWER
900
  • Question 3

Work out the sum of the interior angles of this pentagon in degrees.

(just write the number)

 

CORRECT ANSWER
540
  • Question 4

Work out the sum of the interior angles of this irregular pentagon in degrees.

(just write the number)

 

CORRECT ANSWER
540
  • Question 5

Work out the sum of the interior angles of this octagon in degrees.

(just write the number)

 

CORRECT ANSWER
1080
  • Question 6

What is the sum of the interior angles of any quadrilateral?

(just write the number)

 

 

CORRECT ANSWER
360
  • Question 7

What is the sum of the interior angles of any nonagon (9 sides)?

(just write the number)

 

 

CORRECT ANSWER
1260
  • Question 8

What is the sum of the interior angles of any decagon ?

(just write the number)

 

 

CORRECT ANSWER
1440
  • Question 9

What is the sum of the interior angles of any 12-sided polygon ?

(just write the number)

 

 

CORRECT ANSWER
1800
  • Question 10

What is the sum of the interior angles of any 11-sided polygon ?

(just write the number)

 

 

CORRECT ANSWER
1620
---- OR ----

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