How To Calculate A Polygon’S Sides Using Its Interior Angle?

The sum of interior angles of a regular polygon is determined by subtracting the inside angle from 180 to get the outside angle. The formula for finding the number of sides in a polygon is (n – 2) × 180°, where n is the number of sides of the polygon.

For example, if the inner angle is 165 degrees, subtracting it from 180 would give 15. Dividing 360 by the angle difference and 180 degrees gives 24. The number of sides of a regular polygon can be calculated by using the sum of interior and exterior angles, which are the inside and outside angles. To find the value of an individual interior angle of a regular polygon, one needs to subtract 2 from the number of sides, multiply it by 180, and divide it by… In general, the interior angles of any polygon sum to (number of sides – 2) × 180°. To find the size of one interior angle of a regular polygon, divide the sum by the number of sides.

Each interior angle of a regular polygon of n sides is given by 180(n−2)no. For example, 180(n−2)no=1350, 180(n−2)=135n, 180n−360=135n, and 45n=360.

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 to find sides of a polygon if the interior angle is given?

In order to ascertain the interior angle, the following formula should be employed: i = n – 2 times 180 divided by n, where n represents the number of 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 to find the number of sides of a regular polygon when given the interior angle 140?

The polygon has 9 sides and a single angle of 140°. The sum of interior angles can be calculated by multiplying 140 by the number of sides. Students who received tutoring improved by 1. 19 of a grade on average, 0. 45 more than those without tutoring. This lesson covers interior angles in polygons, how to calculate the sum, and solving problems. Additionally, worksheets are provided for Edexcel, AQA, and OCR exam questions, and further guidance is provided if needed.

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 to find number of sides of a polygon with sum of interior angles?

In order to solve for N, it is necessary to add 360 degrees and then divide 180 degrees on both sides.

How many sides of a regular polygon if each interior angle is 180?

The sum of the interior angles in a polygon is 180 degrees (n – 2), where n is the number of sides in the polygon. Since each angle in a regular polygon is equal, each interior angle has a measure of 180 degrees (n – 2)/n, resulting in 24 sides.

How do you find the sides of a polygon when the interior angle is given?

To solve for n, one must first divide 2 times 180 degrees by n and then multiply the result by n over 1 on both sides. This will result in n being removed from the bottom of the equation. This will guarantee the correct resolution of the equation.

How many sides does a polygon have with an interior angle of 120°?

A regular hexagon is defined as a polygon with six sides, the total of which can be calculated by dividing 360 by the difference between 180 and 120.

How do you find the number of sides of a polygon if each interior angle is 150?

A regular polygon with each interior angle of 150 degrees and exterior angle of 180-150 degrees has 12 sides and is therefore a regular dodecagon with 360/30 sides.

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.