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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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What is a shape with an interior angle of 171?
A shape with an interior angle of 171 degrees is a polygon, specifically one with a high number of sides. For instance, a polygon with 171-degree interior angles could be a 12-sided polygon (dodecagon) or any polygon with more than 12 sides. The interior angle can be calculated using the formula ((n-2) \times 180/n), where (n) is the number of sides, and 171 degrees indicates that the polygon must have at least 12 sides to accommodate such an angle.
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
What is an interior angle of a polygon?
An interior angle of a polygon is the angle formed between two adjacent sides of the polygon that lies inside the shape. For a regular polygon, all interior angles are equal, and their measurement can be calculated using the formula ((n - 2) \times 180^\circ / n), where (n) is the number of sides. Interior angles are crucial for understanding the properties and classifications of polygons.
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 name of the shape that has 12 degrees as its exterior angle?
The shape with an exterior angle of 12 degrees is a dodecagon, which is a polygon with 12 sides. The exterior angle of a regular polygon can be calculated using the formula (360/n), where (n) is the number of sides. For a dodecagon, (360/12 = 30) degrees for each interior angle, which corresponds to 12 degrees for the exterior angle. Thus, the shape is indeed a dodecagon.
What is a shape with an interior angle of 171?
A shape with an interior angle of 171 degrees is a polygon, specifically one with a high number of sides. For instance, a polygon with 171-degree interior angles could be a 12-sided polygon (dodecagon) or any polygon with more than 12 sides. The interior angle can be calculated using the formula ((n-2) \times 180/n), where (n) is the number of sides, and 171 degrees indicates that the polygon must have at least 12 sides to accommodate such an angle.
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
What is an interior angle of a polygon?
An interior angle of a polygon is the angle formed between two adjacent sides of the polygon that lies inside the shape. For a regular polygon, all interior angles are equal, and their measurement can be calculated using the formula ((n - 2) \times 180^\circ / n), where (n) is the number of sides. Interior angles are crucial for understanding the properties and classifications of polygons.
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 name of the shape that has 12 degrees as its exterior angle?
The shape with an exterior angle of 12 degrees is a dodecagon, which is a polygon with 12 sides. The exterior angle of a regular polygon can be calculated using the formula (360/n), where (n) is the number of sides. For a dodecagon, (360/12 = 30) degrees for each interior angle, which corresponds to 12 degrees for the exterior angle. Thus, the shape is indeed a dodecagon.
What shape equals 540?
A shape that has an interior angle sum of 540 degrees is a pentagon, which has five sides. In general, the sum of the interior angles of a polygon can be calculated using the formula ( (n - 2) \times 180 ), where ( n ) is the number of sides. For a pentagon, ( (5 - 2) \times 180 = 540 ) degrees.
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°.
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.
