Question

express the angular measurement of the angle of a regular octagon in degree and radians?​

Answer 1

Given,

The given polygon is a regular octagon.

To find,

The degree measurements of the given polygon in degree and radians.

Solution,

Now,we have to first calculate the sum of the internal angles of the given polygon by using the previously available mathematical formula.

The mathematical formula is,

Sum of the internal angles of a polygon

= 180° × (n-2)

[Here, n = number of sides of the given polygon]

So,the some of the internal angles of the given octagon,

= 180° × (8-2)

= 180° × 6

= 1080°

Measurement of one internal angle of the octagon

= 1080°/8

= 135°

Measurement of one external angle of the octagon

= 180°-135°

= 45°

Radian measurement of one internal angle of the octagon

= 135° × π/180°

= 3π/4 rad

Radian measurement of one external angle of the octagon

= 45° × π/180°

= π/4 rad

Hence,the internal angle of the octagon is 135° or 3π/4 rad and the external angle of the octagon is 45° or π/4 rad.