Each exterior angle of a regular pentagon is 2-3 th of its interior angle . Find the number of sides
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Answer:
regular pentagon
Step-by-step explanation:
EQUATION WORD PROBLEM RATIO AND PROPORTIONS INTERIOR ANGLES EXTERIOR ANGLES
Vanessa N. asked • 04/01/15
The ratio of each exterior angle to each interior angle of a regular polygon is 2:3 find the number of sides
Sum of interior angle of a polygon= (2-n)×180
sum of exterior angles of polygons= 360
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Mark M. answered • 04/01/15
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The measure of each interior angle is (n-2)(180/n) and the measure of each exterior angle is 360/n.
So, 2/3 = 360/n ÷ (n-2)(180/n)
2/3 = 360/n · n/(180n-360)
2/3 = 360/[180(n-2)]
2/3 = 2/(n-2)
Cross multiply: 2(n-2) = 6
2n-4 = 6
2n = 10 So, n = 5
The polygon is a regular pentagon