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The interior angles of a polygon are in AP. The smallest angle is 120° and the common difference is 5°. Find the number of sides of the polygon.
- a)7
- b)9
- c)16
- d)8
Correct answer is option 'B'. Can you explain this answer?
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The interior angles of a polygon are in AP. The smallest angle is 120&...
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The interior angles of a polygon are in AP. The smallest angle is 120&...
Given information:
- Smallest angle = 120°
- Common difference = 5°
Formula:
The sum of the interior angles of a polygon with n sides is given by the formula:
Sum = (n-2) * 180°
Steps to solve:
1. Find the common difference:
Since the smallest angle is 120° and the common difference is 5°, we can find the second smallest angle:
120° + 5° = 125°
2. Find the number of sides:
Let the number of sides be n.
Since the angles are in an AP, we can write the angles in terms of the smallest angle:
120°, 125°, 130°, ...
The sum of the angles of the polygon can be found using the formula:
Sum = (n/2) * (2a + (n-1)d)
Plugging in the values, we get:
(n/2) * (240 + 5(n-1)) = (n-2) * 180
Solving this equation, we get:
5n^2 - 5n - 720 = 0
n^2 - n - 144 = 0
(n-12)(n+12) = 0
n = 12 or n = -12
Since the number of sides cannot be negative, the number of sides of the polygon is 12.
Therefore, the correct answer is option B) 9.
- Smallest angle = 120°
- Common difference = 5°
Formula:
The sum of the interior angles of a polygon with n sides is given by the formula:
Sum = (n-2) * 180°
Steps to solve:
1. Find the common difference:
Since the smallest angle is 120° and the common difference is 5°, we can find the second smallest angle:
120° + 5° = 125°
2. Find the number of sides:
Let the number of sides be n.
Since the angles are in an AP, we can write the angles in terms of the smallest angle:
120°, 125°, 130°, ...
The sum of the angles of the polygon can be found using the formula:
Sum = (n/2) * (2a + (n-1)d)
Plugging in the values, we get:
(n/2) * (240 + 5(n-1)) = (n-2) * 180
Solving this equation, we get:
5n^2 - 5n - 720 = 0
n^2 - n - 144 = 0
(n-12)(n+12) = 0
n = 12 or n = -12
Since the number of sides cannot be negative, the number of sides of the polygon is 12.
Therefore, the correct answer is option B) 9.
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