Question

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

Answer 1

The interior angle of 12-gon is
`150^(\circ)`

The exterior angle of 12-gon is
`30^(\circ)`

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 =
`(360^(\circ))/(number of sides)`

So, exterior angle of 12-gon =
`(360^(\circ))/(n)`

Or, x =
`(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