SOLUTION: Each the interior angle of a regular polygon exceeds the exterior angle by 160 degree .find the number of sides of the polygon
Algebra.Com
Question 329630: Each the interior angle of a regular polygon exceeds the exterior angle by 160 degree .find the number of sides of the polygon
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Each the interior angle of a regular polygon exceeds the exterior angle by 160 degree .find the number of sides of the polygon.
----
Let the exterior angle be "x".
The corresponding interior angle is "x+160"
Equation:
x + x+160 = 180
2x = 20
x = 10 degrees (measure of one of the exterior angles)
-----
Fact: The sum of all of the exterior angles is 360 degrees.
-----
# of exterior angles = 360/10 = 36
---
Therefore, # of sides is 36
=================================
Cheers,
Stan H.
RELATED QUESTIONS
Find the number of sides in a regular polygon if:
the measure of an interior angle... (answered by Theo)
Q1 THE INTERIOR ANGLE OF REGULAR POLYGON EXCEEDS ITS EXTERIOR ANGLE BY 108 HOW MANY... (answered by reviewermath)
If each exterior angle of a regular polygon is 30 degrees , find an interior angle and... (answered by Alan3354)
Each interior angle of a regular polygon is thrice each exterior angle.
Find the number... (answered by Edwin McCravy)
A regular polygon has n sides. The size of each interior angle is 132 degree more than... (answered by Alan3354)
Each interior angle of a regular polygon is 20 more than 3 times the measure of each... (answered by stanbon)
each interior angle of a regular polygon is double of its exterior angle.Find the number... (answered by Alan3354)
Calculate the exterior angle of a regular polygon in which the interior angle is four... (answered by stanbon)
in a regular polygon,each interior angle is greater by 140 degrees than each exterior... (answered by solver91311)