Polygon: Exterior Angles

These four angles
are the interior angles of the quadrilateral.

So
[3x + 40] + [2x + 10] + [120] + [90] = 360.

3x + 2x = 5x
+40 + 10 = +50
+120 + 90 = +210

+50 + 210 = +260

Move +260 to the right side.

Then 5x = 100.

Divide both sides by 5.

Then x = 20.

So x = 20.

A pentagon has 5 sides and 5 angles.

So n = 5.

Set the measure of an exterior angle x.

The measure of an exterior angle is x.

And a regular pentagon has
the same 5 exterior angles.

So 5⋅x = 360.

Divide both sides by 5.

Then x = 72.

Write the unit degree.

So 72º is the answer.

This is a regular pentagon.

It has the same 5 exterior angles.

The measure of an exterior angle is 72.

It says
to find the number of the sides of the polygon.

So the goal is to find n.

The measure of an exterior angle is
60.

The measure of an exterior angle is 60.

And a regular n-gon has
the same n exterior angles.

So n⋅60 = 360.

Divide both sides by 60.

Then n = 6.

So n = 6 is the sides of the polygon.

This is a regular hexagon.
(n = 6)

It has the same 6 exterior angles.

The measure of an exterior angle is 60.