Shape and Space

INTERNAL ANGLES

POLYGON (REGULAR)

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A polygon is a two dimensional shape with straight sides.

There are two types of polygon, regular and irregular.

In a regular polygon each length and angle are equal.

Below is a list of the first six regular polygons

EquilateralTriangle

Square RegularPentagon

RegularHexagon

RegularHeptagon

RegularOctagon

INTERNAL ANGLES

What is the sum of internal angles in a square?

We can divide a square into two triangles

What is the sum of the internal angles of triangle?

180° Two triangles in a square gives a total of

2 × 180 = 360°

Size of one internal angle is

360 ÷ 4 = 90°

90°

90°90°

90°

INTERNAL ANGLES

What is the sum of internal angles in a pentagon?

We can divide a pentagon into three triangles

What is the sum of the internal angles of a triangle?

180°

Three triangles in a pentagon gives a total of

3 × 180 = 540°

Size of one internal angle is540 ÷ 5 = 108°

108°

108°

108°108°

108°

N 2N 2180 N

N

N )2(180

INTERNAL ANGLES

540 ÷ 5 = 108°

360 ÷ 4 = 90°

180 ÷ 3 = 60°

180 × 3 = 540°

180 × 2 = 360°

180 × 1 = 180°

5

4

3

3

2

1

N - agon

Regular Polygon

Number of sides

Divide into how many

triangles?

Sum of internal angles

Size of one angle

Triangle

Square

Pentagon

EXERCISES

1. Calculate the internal angle of a regular nonagon (9 sides).

2. Calculate the internal angle of a regular decagon (10 sides).

3. Calculate the internal angle of a regular hendecagon (11 sides).

4. Calculate the internal angle of a regular dodecagon (12 sides).

What does the internal angle tend to when the number of sides increase?