SOLUTION: sum of interior angels and the sum of exterior angles of polygon are in the ratio 9:2.find the sides of regular polygon.

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Question 1010975: sum of interior angels and
the sum of exterior angles of polygon are in
the ratio 9:2.find the sides of regular
polygon.
Found 2 solutions by mathmate, Theo:
Answer by mathmate(429) (Show Source):
You can put this solution on YOUR website!

Question:
Sum of interior angles and
the sum of exterior angles of polygon are in
the ratio 9:2.find the sides of regular
polygon.

Solution:
Sum of exterior angles, Se= 360 degrees (for any polygon)
Sum of interior angles, Si = 180(n-2) degrees

Given that Si/Se=9/2,
cross multiply and solve for n:
2Si=9Se => 360(n-2)=9*(360) => n-2=9 => n=11

Check:
180(11-2)=9*180
360=2*180
So the ratio is 9:2

Answer:
The number of sides of the given polygon is 11.

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
ratio of the sum of the interior angles to the sum of the exterior angles is 9/2.

i believe you want to find the number of sides in the regular polygon.

the sum of the exterior angles of a polygon is always 360.

the sum of the interior angles of a polygon is equal to (n-2)*180.

since the ratio of the sum of the interior angles of the polygon to the sum of the exterior angles of the polygon is 9/2, your formula would be:

9/2 = ((n-2)*180)/360

cross multiply to get:

9 * 360 = 2 * ((n-2)*180)

simplify to get:

3240 = 2 * (180*n-360)

simplify further to get:

3240 = 360*n-720

add 720 to both sides of this equation to get:

3960 = 360*n

divide both sides of this equation by 360 to get:

n = 11

if we did this correctly, the number of sides of the regular polygon is 11.

the sum of the exterior angles is 360.

the sum of the interior angles is (11-2)*180 = 9*180 = 1620

the ratio of the sum of the interior to the sum of the exterior becomes:

1620 / 360 which is equal to 9/2 if you divide both numerator and denominator by 180.

looks good.

you can also use the cross product to see if the ratios are the same.

9/2 = 1620/360

cross multiply to get 9*360 = 2*1620 which results in 3240 = 3240 which confirms the ratios are the same.