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What is the sum of the measures of the interior angles of a polygon if each exterior angle measures 90 degrees?
Wiki User
∙ 11y ago
The number of exterior angles (and therefore number of sides and number of interior angles) is equal to 360 divided by the measure of each exterior angle. Since the exterior angles measure 90 degrees, the number of sides is 360/90, or 4.
The sum if the interior angles is (180)(s-2), where s is the number of sides. In this cases, it would be (180)(4-2), which is 360 degrees.
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Slightly simpler and more direct:
-- Each interior angle is (180 minus the adjacent exterior angle) = 90 degrees.
-- Since each interior angle is 90 degrees, we immediately recognize the polygon
to be a rectangle, and we remember that the interior angles of any quadrilateral
sum to 360 degrees.
Wiki User
∙ 11y ago
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One exterior angle of a regular polygon measures 30 degrees what is the sum of the polygon's interior angle measures?
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What is the measure of an exterior angle of a regular polygon in which the interior angles measures 150 degrees?
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150 degrees.
What is the measures of the interior angles of a regular polygon if each exterior angle measures 72?
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What is the sum of the polygon's interior angle measures if the exterior angle of a regular polygon's 36 degree?
1440 degrees
What is the sum of the measures of the interior angles of a regular polygon if each exterior angle measures 72?
540 degrees
Find the measures of an interior angle and an exterior angle of a regular polygon with 9 sides?
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