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The interior angle of a regular polygon is 4 times its exterior angle. Find the number of sides?? Give Steps.

Let the number of sides of polygon = nMeasure of each exterior angle = 360°nMeasure of each interior angle = n-2×180°nnow, Measure of each interior angle = 4×Measure of each exterior angle⇒n-2×180°n = 4 × 360°n⇒n-2 = 8⇒n = 10So, number of sides = 10

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10
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10 sides
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10 sides
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Every polygon has total 360 degrees in exterior when added.
So,4 x 360=1440 degrees.
The number of sides=
Let the number of sides be X
(X-2)x180=1440
(X-2)=1440/180=8
X=8+2=10
10 sides.
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exterior angle= 360/n
interior angle= 180- ext angle
let exterior angle be 'x'
4x = 180-x (int and ext angle form a linear pair)
5x=180
x= 36.
36= 360/n
n= 10= no. of sides of polygon
 
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The answer is 10 sides .
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Do you mean  the SUM of all interior  angles of a polygon is 4 times the SUM of all its exterior angles?
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i will try
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let the angles be 4x,x .interior and exterior angles make a linear pair so 4x+x=180 = 5x=180,  x=36
which means the exterior angle is x=36   the sum of all exterior angles are 360 in a polygon and since its regular pultgon , all sides are equal so  y can be the no of sides so,
36y=360 
and y=10 which means the no of sides is 10
 
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