Question

Find the measure of each interior and exterior angle of regular polygon of 12 sides

Answer 1

The total interior angle of a 12 sided polygon is = (12 - 2) 180 degrees = 1800 degrees.The internal angle at each vertex of an regular dodecagon is equal to = 1800 = 150 degrees. ...The total exterior angle of a 12 sided polygon is 360 degrees.

Answer 2

Given:

A polygon of 12 sides

To Find:

Find the measure of each interior and exterior angle

Solution:

To find the measure of each interior angle and exterior we can use formulas as follows,

For exterior angle, the total sum of an exterior angle of a polygon is always 360 degrees so the measure of one exterior angle will be 360/n where n is no of sides of a polygon,

$Each exterior angle=\frac{360}{n}\\=\frac{360}{12} \\=30^{\circ}$

For interior angle, the total sum of all interior angles will be 180*(n-2) where n is the no of sides of a polygon, so the measure of each interior angle will be (n-2)180/n

$Each interior angle=\frac{180(n-2)}{n}\\=\frac{180*(12-2)}{12}\\=\frac{1800}{12}\\=150^{\circ}$

Hence, the measure of each interior angle and exterior angle of a 12 sided polygon will be 150 and 30 degrees respectively.