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

1 answer

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°.