Express in radians as well as in degrees the angle of a regular polygon of 40 sides.?

Question

Answer

Exterior angle= 360/no.of sides
so ext.angle= 360/40
= 9 degree
int. angle = 180-9 = 171 degree
In Radians = 171×π/180
= 19π /20 Radians

Answer

Angle of a Regular Polygon of 40 Sides

A regular polygon has all sides and angles equal. To find the angle of a regular polygon of n sides, we use the formula:

angle = (n-2) x 180 / n

Substituting n=40, we get:

angle = (40-2) x 180 / 40 = 171°

Converting Degrees to Radians

Radians and degrees are two units used to measure angles. One complete circle has 360 degrees or 2π radians. To convert degrees to radians, we use the formula:

radians = degrees x π / 180

Substituting degrees=171, we get:

radians = 171 x π / 180 = 2.98 radians (approx)

Explanation

A regular polygon of 40 sides has 40 equal angles. To find the measure of each angle, we use the formula for the sum of interior angles of a polygon, which is:

sum of interior angles = (n-2) x 180

Substituting n=40, we get:

sum of interior angles = (40-2) x 180 = 6840°

Since a regular polygon has all angles equal, we divide the sum of interior angles by the number of sides:

angle = sum of interior angles / number of sides = 6840° / 40 = 171°

To convert the angle from degrees to radians, we use the conversion formula:

radians = degrees x π / 180

Substituting degrees=171, we get:

radians = 171 x π / 180 = 2.98 radians (approx)

Therefore, the angle of a regular polygon of 40 sides is 171° or 2.98 radians (approx).

Answer

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