46.7k views
4 votes
A polygon has 11 sides. What is the sum of the measure of the interior angles of the polygon? 1800° 1620° 1440° 1980°

User Mehr
by
4.5k points

2 Answers

3 votes

Answer:

1620°

The formula for finding that measure is ...

sum of interior angles of n-sided convex polygon = 180°×(n -2)

For n=11, this is

sum = 180°×9 = 1620°

_____

Another way to get there is to remember that the sum of exterior angles is always 360° for a convex polygon. Then the total (interior + exterior) of the angles of an n-sided polygon is 180°×n. Subtracting the sum of exterior angles gives the total of interior angles: 180°×n -360° = 180°×(n -2).

User Amar Palsapure
by
5.1k points
5 votes

Answer:

1620°

Explanation:

The formula for finding that measure is ...

sum of interior angles of n-sided convex polygon = 180°×(n -2)

For n=11, this is

sum = 180°×9 = 1620°

_____

Another way to get there is to remember that the sum of exterior angles is always 360° for a convex polygon. Then the total (interior + exterior) of the angles of an n-sided polygon is 180°×n. Subtracting the sum of exterior angles gives the total of interior angles: 180°×n -360° = 180°×(n -2).

User Shebelaw
by
6.0k points