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5.1 Regular polygons

3 Work out the following angles, giving reasons.
a the exterior angle of a regular octagon
b the interior angle of a regular octagon

4 A regular polygon has an interior angle of 144°.
Work out:
a the exterior angle
b the number of sides.

5 A regular polygon has an interior angle of 150°.
How many sides does it have?

6 The diagram shows the exterior angle of a regular polygon.
How many sides does the polygon have?

18°

7 The diagram shows part of a regular polygon.
How many sides does the polygon have?

168° 168°

8 Three identical regular polygons are put together at one point.
There is a gap of 36°.
What is the name of the polygon?

36°

9 Three regular polygons fit together at one point without a gap.
One is a square and one is a hexagon.
How many sides does the third shape have?

Hexagon
Square

10 Say, and give a reason, whether each angle is the interior angle of a regular polygon.
If it is, say how many sides the polygon has.
a 110° b 120° c 130° d 140° e 150°

11 A heptagon has seven sides. How large is each interior angle of a regular heptagon?
12 How many sides does a regular polygon have if it has:
a an exterior angle of 5° b an interior angle of 178°?

5 Shapes 43