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What is the number of sides of a regular polygon if one angle measures 171 degrees?
The formula to find the sum of the angles of a polygon is: 180(n - 2)
Since we know that one angle of this regular polygon is 171 degrees, we can find what kind of polygon it will be, using the formula:
180(n - 2) = 171n
180n - 360 = 171n
180n - 171n = 360
9n = 360
n = 360/9
n = 40
Thus the polygon is a 40-sided polygon.
Check:
180(40 - 2) = 180(38) = 6840, which is the sum of the angles of the polygon.
6840/40 = 171 degrees, which is the measure of one of the angles of that polygon .
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What is the number of sides of a regular polygon if one angle measures 140 degrees?
Since the interior angle measure of the regular polygon is 140⁰, its exterior angle measure is 180⁰ - 140⁰ = 40⁰. Since the sum of the exterior angle measures is 360⁰, the polygon has 360⁰/40⁰ = 9 sides.
What is the number of sides of a regular polygon if one angle measures 156?
Interior angle = 156 degrees so exterior angle = 180 - 156 = 24 degrees. Then number of sides = 360 / 24 = 15.
How many sides does a regular polygon have if each angle measures 144 degrees?
We have the interior angle 144∘ . We can find the number of sides using the formula as follows. Thus, the polygon has 10 angles and 10 sides.
The measure of each interior angle of a regular polygon is 144 degrees Find the number of sides of the regular polygon?
It will have 10 equal sides
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.
What is the sum of the measures of the exterior angles of a regular polygon with ten sides?
The sum of the measures of the exterior angles of any polygon, regular or irregular, is always 360 degrees. In a regular polygon with ten sides, each exterior angle measures 360 degrees divided by the number of sides, which in this case is 36 degrees. Therefore, the sum of the measures of the exterior angles of a regular decagon is 10 multiplied by 36 degrees, which equals 360 degrees.
If each exterior angle of a regular polygon measures 40 degrees what is the total number of sides in the polygon?
If each exterior angle of a regular polygon measures 40 degrees, the polygon is a nonagon (9-sided polygon).
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.
How many sides would a regular polygon have if each exterior angle measures 8 degrees?
The sum of the exterior angles of a regular polygon = 360° If an exterior angle measures 8° then the number of sides = 360/8 = 45
What is the number of sides for a polygon whose exterior is 72?
If it's a regular polygon and each exterior angle measures 72 degrees then it is a pentagon which has 5 sides
What is the number of sides of a regular polygon if one of its exterior angles measures 24 degrees?
It is: 360/24 = 15 sides
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 number of sides of a regular polygon if one of its exterior angles measures 8 degrees?
45 sides 360/8 = 45
What is the number of sides of a regular polygon if one angle measures 140 degrees?
Since the interior angle measure of the regular polygon is 140⁰, its exterior angle measure is 180⁰ - 140⁰ = 40⁰. Since the sum of the exterior angle measures is 360⁰, the polygon has 360⁰/40⁰ = 9 sides.
How many sides does a regular polygon have if each exterior angle measures 30 degrees?
The number of sides in a regular polygon can be determined by dividing 360 degrees (the sum of all exterior angles in any polygon) by the measure of each exterior angle. In this case, if each exterior angle measures 30 degrees, the polygon will have 12 sides.
If each interior angle of a regular polygon measures 170 degrees what is the total number of sides in the polygon?
170n = 180n - 360 so 10n = 360 so n = 36
What is the number of sides of a regular polygon if one angle measures 172 degrees?
If one interior angle measures 172° then the corresponding exterior angle measures 180 - 172 = 8°. The number of sides = 360 ÷ 8 = 45.
