 Rollins Size 44mm Exterior Stitched Dutch Falconry Hood US $20.99 
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I have a Polygon(Geometry) Question please help?
These are the three questions i need help with
1. As the number of sides of a regular polygon increases, what happens to:
a. the sum of the exterior angles?
b. the measure of each exterior angle?
2. Dutch claims that he can find the measure of an exterior angle of ANY polygon by simply finding the measure of a central angle and letting the two be equal. Will this method work all the time? Explain or illustrate with an example if this is a reliable method.
10. An exterior angle of a polygon measures 80(degrees). Is the poly gon regular?
Please help i am so stuck thank you
1. As the number of sides of a regular polygon increases, what happens to:
a. the sum of the exterior angles?
Stays the same - always 360°
Try this visualization.
Draw any polygon.
Put your pencil along one side.
Slide it along the side towards the point of the pencil until the other end reaches the vertex.
Now rotate the pencil until it lines up with the next side.
Repeat that process all the way around.
The pencil ends up in its original position, so the rotations totaled a full circle: 360°
(You can do the same thing with the interior angles of a triangle,
and since the pencil ends up pointing in the opposite direction,
it rotated through 180°)
b. the measure of each exterior angle?
There are more of them, so each one gets smaller.
2. Dutch claims that he can find the measure of an exterior angle of ANY polygon by simply finding the measure of a central angle and letting the two be equal. Will this method work all the time? Explain or illustrate with an example if this is a reliable method.
It works for regular polygons.
Draw lines from the center to the vertices.
They form isosceles triangles, and they bisect the interior angles.
Exterior + interior angles = straight angle = 180°
The base angles of the isosceles triangles are (interior angle)/2
so together their sum is an interior angle, and since
total of angles in a triangle = 180° also,
the exterior angle = the central angle.
10. An exterior angle of a polygon measures 80(degrees). Is the polygon regular?
The exterior angles of a regular polygon are all equal and total 360°
So the measure of each must divide 360 evenly.
That is not the case for 80, so the answer is no.
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