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A regular polygon P has 135 diagonals. Find the exterior angle of the polygon P.
- a)180
- b)200
- c)250
- d)300
- e)350
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A regular polygon P has 135 diagonals. Find the exterior angle of the ...
Number of diagonals in a regular polygon =nC2–n
=>nC2–n
=>nC2–n
= 135
=> n = 18
Exterior angle = 360/n
=360/18
=200
=> n = 18
Exterior angle = 360/n
=360/18
=200
Most Upvoted Answer
A regular polygon P has 135 diagonals. Find the exterior angle of the ...
No. of polygons for n sided polygon = n(n-3)/2
Exterior angle of a polygon = 135
n(n-3)/2 = 135
by solving we get n = 18
exterior angle = 360/18
= 20
Exterior angle of a polygon = 135
n(n-3)/2 = 135
by solving we get n = 18
exterior angle = 360/18
= 20
Community Answer
A regular polygon P has 135 diagonals. Find the exterior angle of the ...
To solve this problem, we can use the formula for the number of diagonals in a polygon:
Number of diagonals = n(n-3)/2
where n is the number of sides of the polygon.
Given that the polygon has 135 diagonals, we can set up the equation:
135 = n(n-3)/2
Simplifying this equation, we get:
270 = n^2 - 3n
Rearranging the equation, we have:
n^2 - 3n - 270 = 0
Factoring the quadratic equation, we get:
(n - 18)(n + 15) = 0
So, n = 18 or n = -15.
Since the number of sides of a polygon cannot be negative, we discard n = -15.
Therefore, the polygon has 18 sides.
To find the measure of each exterior angle of the polygon, we can use the formula:
Measure of exterior angle = 360° / n
where n is the number of sides of the polygon.
Substituting n = 18 into the formula, we get:
Measure of exterior angle = 360° / 18 = 20°
Therefore, the correct answer is option B) 200°.
Number of diagonals = n(n-3)/2
where n is the number of sides of the polygon.
Given that the polygon has 135 diagonals, we can set up the equation:
135 = n(n-3)/2
Simplifying this equation, we get:
270 = n^2 - 3n
Rearranging the equation, we have:
n^2 - 3n - 270 = 0
Factoring the quadratic equation, we get:
(n - 18)(n + 15) = 0
So, n = 18 or n = -15.
Since the number of sides of a polygon cannot be negative, we discard n = -15.
Therefore, the polygon has 18 sides.
To find the measure of each exterior angle of the polygon, we can use the formula:
Measure of exterior angle = 360° / n
where n is the number of sides of the polygon.
Substituting n = 18 into the formula, we get:
Measure of exterior angle = 360° / 18 = 20°
Therefore, the correct answer is option B) 200°.
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A regular polygon P has 135 diagonals. Find the exterior angle of the polygon P.a)180b)200c)250d)300e)350Correct answer is option 'B'. Can you explain this answer?
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