Find the sum the interior angle angle measures of a 17-gon

Step-by-step explanation:

Every closed curve called a polygon can be separated into a specific number of triangles. Then, because the sum of the interior angles of a triangle is 180, you take the number of triangles and multiply by 180 to get the sum of the interior angles of the n-gon. To find the number of triangles that exist within an n-gon, subtract 2 from the number of sides. If our figure is a 17-sided polygon, then the number of triangles within it is 17 - 2 = 15. 15 triangles, each with a sum of 180 for its angles. 15 * 180 = 2700.

Each central angle is 360 divided by 17 to get 21°10'35"

Each interior angle is 2700 divided by 17 to get 158°49'24"

2700 degrees.

Step-by-step explanation:

The external angles add up to 360 degrees

So 1 external angle in a regular 17-gon = 360/17

= 21.176 degrees

The internal angle = 180 - 21.176

= 158.824 degrees

Sum of internal angles = 158.824 * 17

= 2700 degrees.