Simple Polygonal Angles

Geometry Level 2

The interior angle of a regular polygon is 30 degrees less than six times the exterior angle.

How many sides does the polygon have?


The answer is 12.

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Sam Cheung by Sam Cheung , 45, United Kingdom

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3 solutions

Sam Cheung
Jan 22, 2015

Let the exterior angle be x. Therefore the interior angle = 6x - 30

x + 6x - 30 = 180 7x = 210 x = 30

Exterior angles add up 360. 360/30 = 12 (regular polygon).

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Ramiel To-ong
Jun 9, 2015

same solution:

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Lu Chee Ket
Jan 22, 2015

x + y = 180

x + 30 = 6 y

7 y = 210

y = 30

n = 360/ 30 = 12

0 Helpful 0 Interesting 0 Brilliant 0 Confused

It would probably help to define x and y.

Sam Cheung - 6 years, 4 months ago

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