the measure of each exterior angle of a regular pentagon is ____ the measure of each exterior angle of a regular nonagon
greater than
less than
equal to**
If i'm wrong can you please explain to me why i'm wrong?
Surely you can see that the exterior angles of regular polygons with a different number of sides cannot be the same. Try drawing something easy, like a square and a pentagon.
As you travel around the outside of a polygon, you keep turning by the same angle. One trip around means you have turned through a full 360°. Thus the more sides, the smaller each turning angle. At each vertex of an n-gon, you make a turn of (360/n)°.
So, a pentagon has greater exterior angles than a nonagon.
Well, if you're looking for an answer that's greater, I'm sorry to say you're "hexed"! The measure of each exterior angle of a regular pentagon is actually equal to the measure of each exterior angle of a regular nonagon. So, you were almost there but just a little off. Don't worry, it's all about those angles!
You are correct, the measure of each exterior angle of a regular pentagon is equal to the measure of each exterior angle of a regular nonagon.
In general, the measure of each exterior angle of a polygon is given by 360 degrees divided by the number of sides of the polygon. So, for both a pentagon and a nonagon, the measure of each exterior angle is 360 degrees divided by the number of sides (5 for a pentagon, 9 for a nonagon), resulting in the same value. Therefore, the measure of each exterior angle of a regular pentagon is equal to the measure of each exterior angle of a regular nonagon.
To determine whether the measure of each exterior angle of a regular pentagon is greater than, less than, or equal to the measure of each exterior angle of a regular nonagon, we need to understand the formulas for calculating the measures of these angles.
The formula for calculating the measure of each exterior angle of a regular polygon is given by:
Measure of each exterior angle = 360° / number of sides
For a regular pentagon with five sides, the measure of each exterior angle would be:
Measure of each exterior angle of a pentagon = 360° / 5 = 72°
For a regular nonagon with nine sides, the measure of each exterior angle would be:
Measure of each exterior angle of a nonagon = 360° / 9 = 40°
Comparing the measures, we can see that the measure of each exterior angle of a regular pentagon (72°) is greater than the measure of each exterior angle of a regular nonagon (40°).
Therefore, the correct answer is: the measure of each exterior angle of a regular pentagon is greater than the measure of each exterior angle of a regular nonagon.
You were correct in selecting "equal to," but the actual relationship between the two measures is that the exterior angle of a regular pentagon is greater than the exterior angle of a regular nonagon.