Regular Polygon With Interior Angle Of 150

12 the sum of a regular polygon s interior angles is always 180 n 2 where n is the number of sides.

Regular polygon with interior angle of 150. The internal angle at each vertex of an regular dodecagon is equal to 150 degrees. One of the interior angles of a regular polygon is 172 and the rest are equal to 158. How many sides does the polygon have angle n 2 180 n 150 n 2 180 n 150n 180n 360 30n 360 n 12.

Each interior angle of the regular polygon is given to be 150. Sum of interior angles of a polygon formula. Each interior angle of a regular n sided polygon is 150 degrees.

Therefore number of sides of polygon 360 each exterior angle 360 30 12. The total interior angle of a 12 sided polygon is 12 2 180 degrees 1800 degrees. The formula for finding the sum of the interior angles of a polygon is devised by the basic ideology that the sum of the interior angles of a triangle is 180 0 the sum of the interior angles of a polygon is given by the product of two less than the number of sides of the polygon and the sum of the interior angles of a triangle.

The number of diagonals is given by the formula nc2 n where nc2 n n 1 1 2 12 11 2 66. Since interior angle exterior angle 180 each exterior angle 30. In a polygon two angles are of 90 each and remaining each angle is of measure 150.

Exterior angles of any polygon always add up to 360 degrees. Therefore for a regular polygon to have interior angles of 150 degrees we use the following. Since an interior angle is 150 degrees its adjacent exterior angle is 30 degrees.

How would one find the number of sides of the polygon.