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If the sum of interior angles of a polygon is 900 degrees, what is the number of diagonals it has?
- a)9
- b)14
- c)20
- d)24
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If the sum of interior angles of a polygon is 900 degrees, what is the...
The sum of interior angles for an ‘n’ sided polygon is
If this value is 900, then the polygon is a heptagon.
The number of diagonals for an ‘n’ sided polygon =
= 14 for a heptagon.
If this value is 900, then the polygon is a heptagon.
The number of diagonals for an ‘n’ sided polygon =
= 14 for a heptagon.
Most Upvoted Answer
If the sum of interior angles of a polygon is 900 degrees, what is the...
Given that sum of Interior angle = 900
We know that exterior angle of a regular polygon = 360
SUM OF ALL THE ANGLES = 900+360
=1260
Number of sides = 180*n = 1260
n = 7
No. of Diagonals = n(n-3)/2
= 7(7-3)/2
= 14
We know that exterior angle of a regular polygon = 360
SUM OF ALL THE ANGLES = 900+360
=1260
Number of sides = 180*n = 1260
n = 7
No. of Diagonals = n(n-3)/2
= 7(7-3)/2
= 14
Community Answer
If the sum of interior angles of a polygon is 900 degrees, what is the...
The sum of the interior angles of a polygon can be calculated using the formula (n-2) * 180 degrees, where 'n' is the number of sides of the polygon. So, in this case, we have:
(n-2) * 180 = 900
Simplifying the equation, we get:
n - 2 = 5
n = 7
Therefore, the polygon has 7 sides.
To find the number of diagonals in a polygon, we can use the formula n * (n-3) / 2, where 'n' is the number of sides. Plugging in the value for 'n', we get:
7 * (7-3) / 2 = 7 * 4 / 2 = 14
Therefore, the polygon has 14 diagonals.
Therefore, the correct answer is option B) 14.
(n-2) * 180 = 900
Simplifying the equation, we get:
n - 2 = 5
n = 7
Therefore, the polygon has 7 sides.
To find the number of diagonals in a polygon, we can use the formula n * (n-3) / 2, where 'n' is the number of sides. Plugging in the value for 'n', we get:
7 * (7-3) / 2 = 7 * 4 / 2 = 14
Therefore, the polygon has 14 diagonals.
Therefore, the correct answer is option B) 14.
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