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Polygons for OCR GCSE Maths

Polygons

This page covers the following topics:

1. Sum of angles in a polygon
2. Pentagons
3. Hexagons
4. Octagons
5. Decagons

The sum of the angles in a polygon can be found by dividing the polygon into triangles and multiplying the number of triangles by 180ยบ. A formula for this is: (n โˆ’ 2) ร— 180ยบ, where n is the number of sides of the polygon.

Sum of angles in a polygon

A pentagon is a five-sided polygon with five angles. The sum of the angles in a pentagon is 540ยบ. The sum of the exterior angles of a pentagon is 360ยบ.

Pentagons

A hexagon is a six-sided polygon with six angles. The sum of the angles in a hexagon is 720ยบ. The sum of the exterior angles of a hexagon is 360ยบ.

Hexagons

An octagon is an eight-sided polygon with eight angles. The sum of the angles in an octagon is 1080ยบ. The sum of the exterior angles of an octagon is 360ยบ.

Octagons

A decagon is a ten-sided polygon with ten angles. The sum of the angles in a decagon is 1440ยบ. The sum of the exterior angles of a decagon is 360ยบ.

Decagons

1

State how many sides and angles an octagon has.

An octagon has 8 sides and 8 angles.

State how many sides and angles an octagon has.

2

Sketch a diagram of a regular pentagon of side 10 cm.

image

Sketch a diagram of a regular pentagon of side 10 cm.

3

Calculate the missing values in the given octagon.

2x = 1080 โˆ’ (160 + 104 + 125 + 100 + 155 + 120), then 2x = 316ยบ, therefore x = 158ยบ.

Calculate the missing values in the given octagon.

4

Sketch a diagram of a regular hexagon of side 8 cm.

image

Sketch a diagram of a regular hexagon of side 8 cm.

5

Calculate the missing angle in the given diagram.

x = 180 โˆ’ 85 = 95ยบ.
So, z = 720 โˆ’ (95 + 110 + 125 + 95 + 120) = 175ยบ.
Therefore, y = 180 โˆ’ 175 = 5ยบ.

Calculate the missing angle in the given diagram.

End of page

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