SOLUTION: 1. If the measure of each of the interior angles of a regular polygon is 100 more than the measure of each of the exterior angles, name the polygon?
2.) Each of the measure of
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Question 118697: 1. If the measure of each of the interior angles of a regular polygon is 100 more than the measure of each of the exterior angles, name the polygon?
2.) Each of the measure of the interior and exterior angles of a regular polygon are in a ration 5:1. Find the measure of an interior and an exterior angle and the name of the polygon.
please help!
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
1) You can use the following facts about polygons to help solve this problem:
a) The sum of an interior angle and an exterior angle is 180 degrees.
b) The measure of an interior angle of a regular polygon of n sides is given by: This works only for "regular" polygons.
In this problem, you have:
"The interior angle is 100 degrees more than the exterior angle"
So you can write:
Substitute
Simplify.
Subtract 100 from both sides.
Divide both sides by 2.
The measure of an exterior angle is 40 degrees.
The measure of an interior angle is 140 degrees.
To find the number of sides (n) in this regular polygon, use:
Substitute to get:
Simplify and solve for n, the number of sides.
Multiply both sides by n.
Add 360 to both sides.
Subtract 140n from both sides.
Divide both sides by 40.
The regular polygon has 9 sides and this is called a "Nonagon"
2) In this problem, you have: "The ratio of an interior angle to an exterior angle is 5:1 Or the interior angle is five times the exterior angle.
Starting with: The sum of the interior and exterior angles is 180 degrees.
Substitute:
Simplify and solve for
Divide both sides by 6.
The exterior angle is 30 degrees.
Substitute
The interior angle is 150 degrees.
Check:
Substitute and
Reduce the fraction on the left side.
To find the number of sides (n), use:
Substitute to get:
Simplify and solve for n. Multiply both sides by n.
Add 360 to both sides.
Subtract 150n from both sides.
Divide both sides by 30.
This regular polygon has 12 sides and is called a "Dodecagon"
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