how do you measure the interior angle and exterior angle of the indicated polygon which is regular 60 gon

The sum of the interior angles is (n-2)180, and each angle will be then 1/60 of that, or each angle will be (n-2)3=58*3 degrees.

The exterior angle will be 180-58*3

To measure the interior and exterior angles of a regular polygon, you need to know the number of sides (also known as the number of vertices) in the polygon.

For a regular polygon with 'n' sides, the formula to find the measure of each interior angle is:

Interior angle measure = (n - 2) * 180 / n

In your case, you mentioned a regular 60-gon (a polygon with 60 sides). So, using the formula:

Interior angle measure = (60 - 2) * 180 / 60
= 3420 / 60
= 57 degrees

Therefore, each interior angle of the regular 60-gon measures 57 degrees.

To find the measure of the exterior angle of a regular polygon, you can use the following formula:

Exterior angle measure = 360 / n

Using the same example of a regular 60-gon:

Exterior angle measure = 360 / 60
= 6 degrees

Hence, each exterior angle of the regular 60-gon measures 6 degrees.