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To find the number of sides ( n ) of a polygon using its interior angle ( A ), you can use the formula for the interior angle of a regular polygon: ( A = \frac{(n-2) \times 180}{n} ). Rearranging this equation, you get ( n = \frac{360}{180 - A} ). By substituting the known value of the interior angle ( A ), you can calculate the number of sides ( n ) of the polygon.
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How many sides does a regular polygon have if the measure of one interior angles is 144?
interior angle = (sides - 2) * 180 / sides sides * interior angle = 180 * sides - 360 sides * (interior angle - 180) = -360 sides = -360 / (interior angle - 180) sides = 360 / (180 - interior angle) So, for 144 degrees: sides = 360 / 36 = 10
How do you find the amount of sides of a shape using it's interior angle?
for a polygon you use order of operations with this equation: [# of side subtracted by 2] multiply by 180= your answer
What is the measure of an angle of 15 side shape?
A 15 sided shape's total number of degrees can be found using the formula (x-2)*180, where x is the number of sides. Using this we find that a 15 sided shape's total degrees is 2340. Divide that number by 15 to get the degrees of each interior angle. It comes out to be 156 degrees.
What is the interior and exterior angle of a 18 sided shape?
For an 18-sided polygon (octadecagon), the formula to calculate the interior angle is ((n-2) \times 180° / n), where (n) is the number of sides. Substituting (n = 18), the interior angle is ((18-2) \times 180° / 18 = 160°). The exterior angle can be found using the formula (360° / n), which gives (360° / 18 = 20°). Therefore, each interior angle is 160° and each exterior angle is 20°.
What is the interior and exterior angle for a regular decagon?
A decagon is a polygon with 10 sides. By using the interior and exterior postulates, you can find the angle measures, which happen to be 144 and 36 degrees respectively.
How many sides does a regular polygon have if the measure of one interior angles is 144?
interior angle = (sides - 2) * 180 / sides sides * interior angle = 180 * sides - 360 sides * (interior angle - 180) = -360 sides = -360 / (interior angle - 180) sides = 360 / (180 - interior angle) So, for 144 degrees: sides = 360 / 36 = 10
How do you find the amount of sides of a shape using it's interior angle?
for a polygon you use order of operations with this equation: [# of side subtracted by 2] multiply by 180= your answer
What is the measure of an angle of 15 side shape?
A 15 sided shape's total number of degrees can be found using the formula (x-2)*180, where x is the number of sides. Using this we find that a 15 sided shape's total degrees is 2340. Divide that number by 15 to get the degrees of each interior angle. It comes out to be 156 degrees.
Equation on how to find no of sides using interior angle 120?
(360) / (180 - n) n= interior angle in this case it will work like this: 360/(180-120) 360/(60) 6, so the number of sides is six.
What is the interior and exterior angle for a regular decagon?
A decagon is a polygon with 10 sides. By using the interior and exterior postulates, you can find the angle measures, which happen to be 144 and 36 degrees respectively.
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.
What is interior angle of a hexadecagon?
The interior angle of a hexadecagon (a polygon with 16 sides) can be calculated using the formula for the interior angle of a regular polygon: ((n - 2) \times 180° / n), where (n) is the number of sides. For a hexadecagon, this is ((16 - 2) \times 180° / 16), which simplifies to (14 \times 180° / 16 = 157.5°). Thus, each interior angle of a regular hexadecagon is 157.5 degrees.
What is the sum of one interior angle of a 36 sided shape?
To find the sum of one interior angle of a 36-sided polygon, you first calculate the total sum of the interior angles using the formula ( (n - 2) \times 180 ), where ( n ) is the number of sides. For a 36-sided polygon, the sum of the interior angles is ( (36 - 2) \times 180 = 34 \times 180 = 6120 ) degrees. To find one interior angle, divide the total by the number of sides: ( \frac{6120}{36} = 170 ) degrees. Thus, each interior angle of a regular 36-sided polygon measures 170 degrees.
How many sides does a polygon have when the measure of each interior angle is 144?
A regular polygon with interior angles of 144 degrees has 10 sides. Using the fact that a regular n-gon has interior angles of degree (n-2)*180/n, you can solve for the number of sides fairly easily.
What is the size an angle in a polygon?
The size of an angle in a polygon depends on the number of sides the polygon has. The sum of the interior angles of a polygon can be calculated using the formula ( (n - 2) \times 180^\circ ), where ( n ) is the number of sides. To find the measure of each interior angle in a regular polygon (where all angles are equal), divide the total sum by the number of sides. For example, a triangle has a total interior angle sum of ( 180^\circ ), while a quadrilateral has ( 360^\circ ).
What is the interior and exterior angle a regular 10 sided polygon?
In a regular 10-sided polygon, each interior angle measures 144 degrees. This can be calculated using the formula: (n-2) x 180 / n, where n is the number of sides. The exterior angle of a regular polygon is always supplementary to the interior angle and can be calculated by subtracting the interior angle from 180 degrees. Therefore, the exterior angle of a regular 10-sided polygon would be 36 degrees.
What is the angle measures of an interior angle for a pentagon?
The measure of an interior angle of a regular pentagon can be calculated using the formula ((n - 2) \times 180^\circ / n), where (n) is the number of sides. For a pentagon, (n = 5), so the interior angle measures ((5 - 2) \times 180^\circ / 5 = 108^\circ). Therefore, each interior angle of a regular pentagon measures 108 degrees.
