one external angle of a regular polygon is 18°. (a) what is the sum of its external angle?(b) how many sides does it have?(c) what is the sum of internal angles?
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The sum of the measures of the interior angle of any polygon is the number of sides minus 2 multiplied by 180. A polygon with 18 sides has an interior angle sum of 2880 degrees.
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(a) Find the sum of Exterior Angles:
Sum of exterior angles is always 360º, regardless of the number of sides the polygon has.
(b) Find the number of sides the polygon has:
Sum of all angles = 360
one angle = 18
Number of sides = sum of all angles ÷ size of one angle
Number of sides = 360 ÷ 18 = 20
The polygon has 20 sides
(c) Find the sum of interior angles:
Sum of interior angles = (n - 2) x 180 where no is the number of sides
Sum of interior angles = (20 - 2) x 180 = 3240º
Answer: (a) 360º (b) 20 sides (c) 3240º
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