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If the interior angle of a regular polygon exceeds the exterior angle by 132o, then the number of sides of the polygon is:
Correct answer is '15'. Can you explain this answer?
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If the interior angle of a regular polygon exceeds the exterior angle...
Solution:
Let the exterior angle of the polygon be x.
Then, the interior angle of the polygon will be (x + 132) degrees.
We know that the sum of the exterior angles of a polygon is 360 degrees.
As the polygon is regular, all exterior angles will be equal.
Therefore, we can write:
n * x = 360, where n is the number of sides of the polygon.
We also know that the sum of the interior angles of a polygon with n sides is given by:
(n - 2) * 180
As the polygon is regular, all interior angles will be equal.
Therefore, we can write:
n * (x + 132) = (n - 2) * 180
Simplifying this equation, we get:
nx + 132n = 180n - 360
48n = 360 + 132n
48n - 132n = 360
-84n = 360
n = -4.28
Since n must be a positive integer, we can conclude that the number of sides of the polygon is 15.
Therefore, the correct answer is 15.
Let the exterior angle of the polygon be x.
Then, the interior angle of the polygon will be (x + 132) degrees.
We know that the sum of the exterior angles of a polygon is 360 degrees.
As the polygon is regular, all exterior angles will be equal.
Therefore, we can write:
n * x = 360, where n is the number of sides of the polygon.
We also know that the sum of the interior angles of a polygon with n sides is given by:
(n - 2) * 180
As the polygon is regular, all interior angles will be equal.
Therefore, we can write:
n * (x + 132) = (n - 2) * 180
Simplifying this equation, we get:
nx + 132n = 180n - 360
48n = 360 + 132n
48n - 132n = 360
-84n = 360
n = -4.28
Since n must be a positive integer, we can conclude that the number of sides of the polygon is 15.
Therefore, the correct answer is 15.
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Community Answer
If the interior angle of a regular polygon exceeds the exterior angle...
Given,
Interior angle - Exterior angle =132o
Measurement of each interior angle = n−2 / n × 180
Measurement of each exterior angle = 360∘ / n
According to the question:
By Cross multiplication:
180n − 360 − 360 = 132n
48n = 720
N = 15
∴ The number of sides in a polygon is 15.
Hence, the correct answer is 15.
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If the interior angle of a regular polygon exceeds the exterior angle by 132o, then the number of sides of the polygon is:Correct answer is '15'. Can you explain this answer?
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If the interior angle of a regular polygon exceeds the exterior angle by 132o, then the number of sides of the polygon is:Correct answer is '15'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If the interior angle of a regular polygon exceeds the exterior angle by 132o, then the number of sides of the polygon is:Correct answer is '15'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the interior angle of a regular polygon exceeds the exterior angle by 132o, then the number of sides of the polygon is:Correct answer is '15'. Can you explain this answer?.
If the interior angle of a regular polygon exceeds the exterior angle by 132o, then the number of sides of the polygon is:Correct answer is '15'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If the interior angle of a regular polygon exceeds the exterior angle by 132o, then the number of sides of the polygon is:Correct answer is '15'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the interior angle of a regular polygon exceeds the exterior angle by 132o, then the number of sides of the polygon is:Correct answer is '15'. Can you explain this answer?.
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