Question

in the diagram, suppose one of the sides had an extended line, creating an exterior angle. what would be the approximate degree measure of the exterior angle?

(1 point)
responses

140°
140°

40°
40°

147.3°
147.3°

32.7°

the image is an 11 sided polygon

Answer 1

To find the exterior angle of a polygon, you can use the formula for the sum of the exterior angles of any polygon, which is always 360 degrees, regardless of the number of sides.

For a regular polygon (where all sides and angles are equal), the measure of each exterior angle can be calculated by dividing 360 degrees by the number of sides (n):

\[
\text{Exterior angle} = \frac{360°}{n}
\]

In your case, for an 11-sided polygon (n = 11):

\[
\text{Exterior angle} = \frac{360°}{11} \approx 32.73°
\]

So, the approximate degree measure of the exterior angle of the 11-sided polygon would be about **32.7°**.

Thus, the correct response would be **32.7°**.