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Find the number of sides of a regular polygon in which the exterior angle is one sixth the interior angle.
- a)12
- b)15
- c)13
- d)14
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Find the number of sides of a regular polygon in which the exterior an...
Understanding Interior and Exterior Angles
In a regular polygon, the relationship between the interior angle (I) and the exterior angle (E) is crucial. The sum of an interior angle and its corresponding exterior angle is always 180 degrees.
Given Condition
According to the problem, the exterior angle is one sixth of the interior angle:
E = (1/6) * I
This can be rearranged to express the interior angle in terms of the exterior angle:
I = 6E
Relationship Between Interior and Exterior Angles
Using the relationship between interior and exterior angles:
I + E = 180
Substituting I from the previous equation:
6E + E = 180
This simplifies to:
7E = 180
Calculating the Exterior Angle
Now, we can find the measure of the exterior angle:
E = 180 / 7
Finding the Number of Sides
The exterior angle of a regular polygon is also calculated using the formula:
E = 360 / n
where n is the number of sides.
Setting the two expressions for E equal gives:
360 / n = 180 / 7
Cross-multiplying leads to:
360 * 7 = 180n
Simplifying this, we find:
2520 = 180n
Solving for n:
n = 2520 / 180 = 14
Conclusion
The regular polygon with an exterior angle that is one sixth of the interior angle has 14 sides. Therefore, the correct answer is option 'D'.
In a regular polygon, the relationship between the interior angle (I) and the exterior angle (E) is crucial. The sum of an interior angle and its corresponding exterior angle is always 180 degrees.
Given Condition
According to the problem, the exterior angle is one sixth of the interior angle:
E = (1/6) * I
This can be rearranged to express the interior angle in terms of the exterior angle:
I = 6E
Relationship Between Interior and Exterior Angles
Using the relationship between interior and exterior angles:
I + E = 180
Substituting I from the previous equation:
6E + E = 180
This simplifies to:
7E = 180
Calculating the Exterior Angle
Now, we can find the measure of the exterior angle:
E = 180 / 7
Finding the Number of Sides
The exterior angle of a regular polygon is also calculated using the formula:
E = 360 / n
where n is the number of sides.
Setting the two expressions for E equal gives:
360 / n = 180 / 7
Cross-multiplying leads to:
360 * 7 = 180n
Simplifying this, we find:
2520 = 180n
Solving for n:
n = 2520 / 180 = 14
Conclusion
The regular polygon with an exterior angle that is one sixth of the interior angle has 14 sides. Therefore, the correct answer is option 'D'.
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Community Answer
Find the number of sides of a regular polygon in which the exterior an...
Let the number of sides of the polygon be n.
Each exterior angle= 360/n
Each interior angle of this polygon=
As per the question,
⇒ (n - 2) 30 =360
⇒ n-2= 12
.'. n= 14.
Each exterior angle= 360/n
Each interior angle of this polygon=
As per the question,
⇒ (n - 2) 30 =360
⇒ n-2= 12
.'. n= 14.
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Find the number of sides of a regular polygon in which the exterior angle is one sixth the interior angle.a)12b)15c)13d)14Correct answer is option 'D'. Can you explain this answer?
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Find the number of sides of a regular polygon in which the exterior angle is one sixth the interior angle.a)12b)15c)13d)14Correct answer is option 'D'. 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 Find the number of sides of a regular polygon in which the exterior angle is one sixth the interior angle.a)12b)15c)13d)14Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the number of sides of a regular polygon in which the exterior angle is one sixth the interior angle.a)12b)15c)13d)14Correct answer is option 'D'. Can you explain this answer?.
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