Question

Express in radians and also in degrees the angles of a regular polygon of 40 sides and of n sides

Answer 1

So for calculating the interior angles of a regular polygon ,we need to know about the sum of interior angles first

So the sum of interior angle of a regular n sided regular polygon is
(n-2)180

A polygon is said to be regular if and only if the n sides are equal in length else it is said to be irregular polygon

Now as the n sides are equal in length the measure of each of the interior angle of the polygon can be found by dividing the total angle sum by the number of sides

So for any n sided regular polygon the interior angle is given by formula
(n-2)* (180/n)

To convert into radians multiply the above term by (pi/360)

So the term will change to (n-2)*(pi/2n)

As in the question there is a 40 sided regular polygon so each of interior angle  will be
38*(180/40)
=171 degrees

Answer 2

Number of sides of the Regular Polygon = 40

Each interior angle of the Polygon is given by,
 (n - 2) × 180/n
= (40 - 2) × 180/40
= 38 × 18/4
= 19 × 9
= 171°


Now, Let us convert it in Radians.

 ∵ π rad = 180°
∴ 1° = π/180 rad.
∴ 171° = (171/180)π rad.
   = 57π/60 rad.


Hope it helps.