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Solve the following question and mark the best possible option.
In a convex polygon, all internal angles are distinct integers (in degree measure). The largest angle is 110°. The number of sides of the polygon can be
  • a)
    8
  • b)
    7
  • c)
    6
  • d)
    5
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Solve the following question and mark the best possible option.In a co...
Since greatest internal angle is 110º so, least external angle = 180º - 110º = 70º for the polygon to have the maximum no. of sides, the angles must be as close as possible. Also, sum of external angles = 360º
So, external angles can be, 70º , 71º, 72º, 73º, 74º polygon can have max 5 sides
So, choice 4.
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Most Upvoted Answer
Solve the following question and mark the best possible option.In a co...
Let the number of sides of the polygon be n.
The sum of the internal angles in a polygon with n sides is given by the formula (n-2) * 180 degrees.
Since all the internal angles are distinct integers, we can assume that the smallest angle is 1 degree.
The largest angle is given to be 110 degrees.
Therefore, the sum of all the internal angles is 1 + 2 + 3 + ... + 110 = (110 * 111) / 2 = 6105 degrees.
Using the formula (n-2) * 180 = 6105, we can solve for n:
(n-2) * 180 = 6105
n-2 = 6105 / 180
n-2 = 33.9167
n ≈ 35.9167
Since the number of sides of a polygon must be a whole number, the best possible option is 36 sides.
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Solve the following question and mark the best possible option.In a convex polygon, all internal angles are distinct integers (in degree measure). The largest angle is 110°. The number of sides of the polygon can bea)8b)7c)6d)5Correct answer is option 'D'. Can you explain this answer?
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