Polygons for SQA National 5 Maths
This page covers the following topics:
1. Sum of angles in a polygon
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.
State how many sides and angles an octagon has.
An octagon has 8 sides and 8 angles.
Sketch a diagram of a regular pentagon of side 10 cm.
Calculate the missing values in the given octagon.
2x = 1080 − (160 + 104 + 125 + 100 + 155 + 120), then 2x = 316º, therefore x = 158º.
Sketch a diagram of a regular hexagon of side 8 cm.
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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