# StudySquare

# Polygons for SQA National 5 Maths

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 180º. A formula for this is: (n − 2) × 180º, where n is the number of sides of the polygon.

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

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

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

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

# 1

State how many sides and angles an octagon has.

An octagon has 8 sides and 8 angles.

# 2

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

image

# 3

Calculate the missing values in the given octagon.

2x = 1080 − (160 + 104 + 125 + 100 + 155 + 120), then 2x = 316º, therefore x = 158º.

# 4

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

image

# 5

Calculate the missing angle in the given diagram.

x = 180 − 85 = 95º.

So, z = 720 − (95 + 110 + 125 + 95 + 120) = 175º.

Therefore, y = 180 − 175 = 5º.

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