How do you prove that the sum of the exterior angles of a polygon is 360?

Let sum of all exterior angles be ‘E’, and sum of all interior angles be ‘I’. E = n × 180° – (n -2) × 180°. Hence, The sum of all the exterior angles of a polygon is 360° .

What is supplementary to an interior angle of the polygon?

Answer: Supplementary angle to any of the interior angles of a regular polygon = 180º – [(n – 2) × 180º] / n. For a regular polygon, all interior angles are equal so we can calculate the supplementary angle to any one of the interior angles.

Why do the exterior angles of a polygon always sum to 360 degrees?

The sum of the exterior angles of any polygon (remember only convex polygons are being discussed here) is 360 degrees. Because the exterior angles are supplementary to the interior angles, they measure, 130, 110, and 120 degrees, respectively. Summed, the exterior angles equal 360 degreEs.

Is it possible to have a regular polygon each of whose interior angle is 140 degree?

Answer: Each interior angle of a regular polygon = 140 deg. So each exterior angle of the regular polygon = 180-140 = 40 deg. Hence the regular polygon has 360/40 = 9 sides.

How do you prove the sum of the exterior angles of an angle?

The sum of the interior angles of a regular polygon with n sides is 180(n-2). So, each interior angle has measure 180(n-2) / n. Each exterior angle is the supplement to an interior angle. Sum of exterior angles = n(360 / n) = 360.

How do you find the sum of an exterior angle?

Regular Polygons The sum of the exterior angles of a regular polygon will always equal 360 degrees. To find the value of a given exterior angle of a regular polygon, simply divide 360 by the number of sides or angles that the polygon has.

What is a polygon interior angle?

In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint. For a simple (non-self-intersecting) polygon, regardless of whether it is convex or non-convex, this angle is called an interior angle (or internal angle) if a point within the angle is in the interior of the polygon.

How do you find the angle measure of an irregular polygon?

The interior angles in an irregular polygon are not equal to each other. Therefore, to find the sum of the interior angles of an irregular polygon, we use the formula the same formula as used for regular polygons. The formula is: Sum of interior angles = (n − 2) × 180° where ‘n’ = the number of sides of a polygon.

How do you find the interior and exterior angles of a polygon?

The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides. The sum of exterior angles of a polygon is 360°. The formula for calculating the size of an exterior angle is: exterior angle of a polygon = 360 ÷ number of sides.