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How do you find the measure of each interior angle of a regular polygon that has 135 diagonals?
Wiki User
∙ 11y ago
First find the number of sides of the polygon and let it be x:
Rearrange the diagonal formula: 0.5*(x2-3x) = 135 into a quadratic equation
Which is: x2-3x-270 = 0 and solving the equation gives x positive value of 18
Therefore the polygon has 18 sides
Sum of interior angles: (18-2)*180 = 2880 degrees
Each interior angle: 2880/18 = 160 degrees
Wiki User
∙ 11y ago
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Only if the polygon is "regular".
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13 1/3 °
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Only if the polygon is "regular".
Is Each of the interior angles in a polygon are equal in measure.?
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A pentagon (five sided regular polygon) has interior angles of 108°.
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What is the size of each interior angle of a regular polygon that has 27 diagonals?
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Which regular polygon has interior angles that measure about 152.3 degrees each?
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The interior angle of an octdecagon, an 18 sided regular polygon, is 160o.
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A regular polygon with 4 sides is a square. The measure of any interior angle of a square is 90 degrees.
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A regular octadecagon (an eighteen sided polygon) would have nine diagonals.
