How To Determine A Regular Polygon’S Sides Given Its Interior Angle?

The sum of interior angles of a regular polygon is given by the formula 180(n-2)/n, where n is the number of sides of the polygon. Each angle (of a regular polygon) is given by (n – 2) × 180 °/n.

To find the number of sides in a polygon, one can use the formula: Sum of Interior Angles = (n – 2) × 180 °. For example, to find the size of each interior angle for a regular decagon, one can subtract the inside angle from 180 to get the outside angle. This gives us 24 sides.

To find the value of an individual interior angle of a regular polygon, one needs to subtract 2 out of the number of sides, multiply it by 180, and divide it by the sum of exterior angles. In this case, the number of sides of a regular polygon is 24.

The number of sides of a regular polygon can be calculated by using the interior and exterior angles, which are, respectively, the inside and outside angles. Each interior angle of a regular polygon of n sides is given by 180(n-2)n degree.

In summary, finding the number of sides of a regular polygon with one interior angle is a simple process that involves dividing the sum of interior angles by the number of sides. By doing so, we can determine the number of sides in a regular polygon and its composition.

How to find the number of sides of a regular polygon when given the interior angle is 150?

The interior angle of a polygon is 150 degrees, and its adjacent exterior angle is 30 degrees. The exterior angles of a polygon are always additive, thus 360 degrees is divided by 30 to yield 12 sides.

How to find the number of sides of a regular polygon when given the interior angle is 165?

The interior angle of a polygon with 24 sides and a typical angle of 165 degrees is calculated to be 360 degrees. The exterior grade of regular polygons is then aggregated at 360 degrees, resulting in a total of 24 sides. The exterior angle of a polygon is 180 degrees minus 165 degrees, or 15 degrees. It follows that the sum of the number of sides in a polygon is 360 degrees.

How do you find the sides of a polygon with an interior angle?

In order to ascertain the exterior angle, it is necessary to subtract the interior angle from 180° and then divide 360° by the exterior angle. To illustrate, if the interior angle is 108°, the exterior angle is 72°, resulting in a pentagon with five sides.

How many sides does a polygon have with an interior angle of 162?

The sum of the interior and exterior angles of a regular polygon is 180°, and since each interior angle is 162°, the sum of all exterior angles is 360°. It can therefore be concluded that the number of sides of a regular polygon is 20.

How many sides does a polygon have if the interior angle is 162?

The given polygon has 20 sides due to the fact that its interior angles are 162° and its exterior angles are 180° minus 162°, which is equal to 18°. The sum of these angles is 180°, and the sum of all exterior angles is always 360°, as each exterior angle is 18°. It can thus be concluded that the number of sides of the polygon is 20.

How many sides does a polygon have if each interior angle is 120?

The sum of the interior angles of a regular polygon is equal to (n – 2) × 180°, where n is the number of sides in the polygon. This simplifies to ((n – 2) × 180°) / n, which is the angle of a hexagon with 6 sides.

How to find the number of sides of a regular polygon when given the interior angle is 160?

The number of sides in a regular polygon with every interior angle (i) 160° is 18, and (ii) 150° is 12 is determined by dividing the interior angle by the number of sides.

How many sides has a regular polygon whose interior angle is 135?

The number of sides of a regular polygon with an interior angle of 135° is 8. The sum of the interior angles of a polygon with n sides is (n – 2) x 180°, which is equal to 8.

What is the rule for interior angle of polygon?

The sum of the interior angles of a polygon is calculated using the formula (n – 2) × 180°, where n is the number of sides. A regular polygon is defined as one in which all angles are equal and all sides are of equal length. In order to ascertain the sum of the interior angles, it is necessary to divide the polygon into triangles, the sum of whose angles is 180°. In order to ascertain the magnitude of an interior angle, it is necessary to multiply the number of triangles that comprise the polygon by 180°.

How many sides does a polygon have with an interior angle of 108?

A regular polygon, designated a pentagon, exhibits an interior angle of 108° and is calculated by adding the sum of the interior angles of a regular polygon, which is equivalent to (n – 2) × 180°/n, where n represents the number of sides in the polygon.

How many sides does a regular polygon with 156 interior angles have?

A regular polygon with an interior angle of 156° has 15 sides.