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Interior Angle Sums in Polygons

In this worksheet, students apply their knowledge of triangles to calculate the number of sides in a polygon given the sum of its interior angles.

'Interior Angle Sums in Polygons' worksheet

Key stage:  KS 4

Curriculum topic:  Geometry and Measures

Curriculum subtopic:  Apply Pythagoras' Theorem and Trigonometric Ratios to Find Angles and Lengths in 2D Figures

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

The sum of the interior angles in a polygon increases as the number of sides increases.

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

 

Let's look at this hexagon.

 

 

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.

 

No. of triangles = No. of sides - 2

 

Example

Find the number of sides in a polygon whose interior angle sum is 720º.

 

Answer

720 ÷ 180 = 4

No. of sides = No. of triangles + 2

No. of sides = 4 + 2 = 6

Find the number of sides in a polygon whose interior angle sum is 180º.

Find the number of sides in a polygon whose interior angle sum is 540º.

Find the number of sides in a polygon whose interior angle sum is 360º.

Find the number of sides in a polygon whose interior angle sum is 1080º.

Find the number of sides in a polygon whose interior angle sum is 1440º.

Find the number of sides in a polygon whose interior angle sum is 900º.

Find the number of sides in a polygon whose interior angle sum is 1800º.

Find the number of sides in a polygon whose interior angle sum is 2340º.

Find the number of sides in a polygon whose interior angle sum is 4500º.

Find the number of sides in a polygon whose interior angle sum is 10440º.

  • Question 1

Find the number of sides in a polygon whose interior angle sum is 180º.

CORRECT ANSWER
3
EDDIE SAYS
180 ÷ 180 + 2
  • Question 2

Find the number of sides in a polygon whose interior angle sum is 540º.

CORRECT ANSWER
5
EDDIE SAYS
540 ÷ 180 + 2
  • Question 3

Find the number of sides in a polygon whose interior angle sum is 360º.

CORRECT ANSWER
4
EDDIE SAYS
360 ÷ 180 + 2
  • Question 4

Find the number of sides in a polygon whose interior angle sum is 1080º.

CORRECT ANSWER
8
EDDIE SAYS
1080 ÷ 180 + 2
  • Question 5

Find the number of sides in a polygon whose interior angle sum is 1440º.

CORRECT ANSWER
10
EDDIE SAYS
1440 ÷ 180 + 2
  • Question 6

Find the number of sides in a polygon whose interior angle sum is 900º.

CORRECT ANSWER
7
EDDIE SAYS
900 ÷ 180 + 2
  • Question 7

Find the number of sides in a polygon whose interior angle sum is 1800º.

CORRECT ANSWER
12
EDDIE SAYS
1800 ÷ 180 + 2
  • Question 8

Find the number of sides in a polygon whose interior angle sum is 2340º.

CORRECT ANSWER
15
EDDIE SAYS
2340 ÷ 180 + 2
  • Question 9

Find the number of sides in a polygon whose interior angle sum is 4500º.

CORRECT ANSWER
27
EDDIE SAYS
4500 ÷ 180 + 2
  • Question 10

Find the number of sides in a polygon whose interior angle sum is 10440º.

CORRECT ANSWER
60
EDDIE SAYS
10440 ÷ 180 + 2
---- OR ----

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