Question

The interior angle of a regular polvgon is 9 times the size of its exterior angle

Work out how many sides the polygon has

Answer 1

Answer: 20 sides

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Work Shown:

x = exterior angle

9x = interior angle

interior + exterior = 180

9x+x = 180

10x = 180

x = 180/10

x = 18

n = number of sides

n = 360/x

n = 360/18

n = 20

There are 20 sides to the regular polygon.

Side notes:

• The formula to determine n only works for regular polygons.
• A polygon with 20 sides is known as an icosagon.
• Any pair of adjacent interior and exterior angles are supplementary. They add to 180 degrees.