Question

Find the measures of an interior angle and an exterior angle of a regular 12-gon

Answer 1

Answer:

The interior angle of 12-gon is $150^{\circ}$  

The exterior angle of 12-gon is $30^{\circ}$

Step-by-step explanation:

Given as :

A regular 12-gon is a dodecagonal polygon

i.e The number of sides of the polygon = n = 12

Let The exterior angle of 12-gon = x°

And Let The interior angle of 12-gon = y°

Now,

∵ Exterior angle = $\frac{360^{\circ}}{number of sides}$

So, exterior angle of 12-gon = $\frac{360^{\circ}}{n}$

Or, x = $\frac{360^{\circ}}{12}$

∴ x = $30^{\circ}$

So,The exterior angle of 12-gon = x = $30^{\circ}$

Again

∵ Interior angle = $180^{\circ}$ - exterior angle

So, interior angle of 12-gon = $180^{\circ}$ - exterior angle

Or, y =  $180^{\circ}$ -  $30^{\circ}$

∴ y =  $150^{\circ}$

So,The interior angle of 12-gon = y = $150^{\circ}$

Hence, The interior angle of 12-gon is $150^{\circ}$ and The exterior angle of 12-gon is $30^{\circ}$ . Answer