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If the interior angle of a regular polygon is 13 times the size of a diagnol angle - how many sides does the polygon have?
Wiki User
∙ 13y ago
The interior angle (A) of a regular polygon is bisected by a diagonal. Therefore two diagonals and one side form an isosceles triangle with two base angles each measuring ½ A. The diagonal angle (at the centre) is thus 180 - A.
We then have A = 13(180 -A) : A = 180 x 13/14
The sum of the interior angles of a regular polygon = 2n - 4 right angles = 90(2n - 4)° where n is the number of sides.
Each interior angle (A) = 90(2n - 4) ÷ n = 180 x 13/14 : 180n - 360 = 180n x 13/14 : 180n/14 = 360 : n = 14 x 360/180 = 28
The polygon has 28 sides.
Wiki User
∙ 13y ago
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How many sides does a regular polygon if its interior angles are 270?
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How do you measure sides of a regular polygon if each interior angle is 120?
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If the measure of one interior angle of a regular polygon is 90 degrees how many sides does the polygon have?
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