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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?
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.
What else can I help you with?
What is the sum of the measures of the interior angles of a polygon if each exterior angle measures 120 degrees?
The 3 interior angles of this equilateral triangle will add up to 180 degrees
What is the measure of an angle of a REGULAR 32-gon polygon?
Each exterior angle measures 11.5 degrees. Each interior angle measures 168.75 degrees
What is the sum of the measures of the interior angles of a regular polygon if each exerior angle measures 72 degrees?
There are 5 interior angles and each one measures 108 degrees (180-72). Since the sum of exterior angles of any polygon is 360⁰, then that polygon would have 5 angles (360/72). So the sum of interior angle measures is 540⁰.
What is the sum of angle measures of a 13-sided polygon?
Sum of exterior angles = 360 degrees Sum of interior angles = 1980 degrees
What is the measure of each angle of a regular polygon with 7 sides?
A regular polygon has sides of equal length, as well as interior angles of equal measure. But for any regular polygon, the sum of the measures of the exterior angles is 360 degrees. You can use this information to find out the measure of an interior angle, because the sum of the measures of each interior/exterior pair of angles is always 180 degrees. So to find the answer to this problem, divide 360 by 7. Each exterior angle is about 51.4 degrees. Subtract that number from 180. Each interior angle is about 128.6 degrees.
One exterior angle of a regular polygon measures 30 degrees what is the sum of the polygon's interior angle measures?
1800 degrees
One exterior angle of a regular polygon measures 36 What is the sum of the polygon's interior angle measures?
1440 degrees
One exterior angle of a regular polygon measures 36. What is the sum of the polygon's interior angle measures?
1440 degrees
What is the measures of an interior angle and an exterior angle of a regular polygon with 6 sides?
Interior angle = 120 degrees Exterior angle = 60 degrees
What is the measure of the interior angle and the exterior angle of a regular polygon with 20 sides?
Each exterior angle measures 20 degrees Each interior angle measures 160 degrees
What is the sum of the measures of the interior angles of a regular polygon if each exterior angle measures 72 degrees?
540 degrees
What is the measure of an exterior angle of a regular polygon in which the interior angles measures 150 degrees?
30 degrees
An exterior angle of a regular polygon measures 30 degrees What is the measure of an interior angle?
150 degrees.
What is the measures of the interior angles of a regular polygon if each exterior angle measures 72?
The interior angle of any regular polygon can be calculated using the formula 180 * (n - 2) / n, where n is the number of sides. In this case, since each exterior angle measures 72 degrees, the interior angle would be 180 - 72 = 108 degrees. So the measures of the interior angles in this regular polygon would be 108 degrees.
One exterior angle of a regular polygon measures 40 What is the sum of the polygon's interior angle measures?
The sum of a regular polygon's interior angles is always equal to (n-2) * 180, where n is the number of sides in the polygon. Given that one exterior angle measures 40 degrees, we can find the interior angle by subtracting 40 from 180 degrees (since the exterior and interior angles are supplementary) to get 140 degrees. So, the sum of the interior angles of the regular polygon is 140 * n.
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
