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.
Algebra.Com
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.
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