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Consider the following
The interior angles of a polygon of n sides are in AP. The smallest angle is 120° and the common difference is 5°.
Q. What is the largest interior angle of the polygon?
- a)160° only
- b)195° only
- c)Either 160° or 195°
- d)Nither 160 nor 195°
Correct answer is option 'A'. Can you explain this answer?
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Consider the followingThe interior angles of a polygon of n sides are ...
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Consider the followingThe interior angles of a polygon of n sides are ...
Explanation:
Given Information:
- Smallest angle of the polygon = 120°
- Common difference between interior angles = 5°
Concept:
- The sum of interior angles of a polygon with n sides is given by the formula (n-2)*180°.
- In an arithmetic progression, the sum of angles is equal to the number of sides multiplied by the average of the first and last angles.
Finding the Largest Angle:
- Let the largest angle be x°.
- Since the smallest angle is 120° and the common difference is 5°, the second smallest angle is 120 + 5 = 125°.
- The average of the first and last angles in an AP is (120 + x)/2.
- The sum of angles of the polygon with n sides is n*(120 + x)/2.
- This sum is also equal to (n-2)*180°.
- Equating the two expressions for the sum of angles, we get: n*(120 + x)/2 = (n-2)*180
- Solving this equation, we get x = 160°.
Conclusion:
- Therefore, the largest interior angle of the polygon is 160°.
- Hence, the correct answer is option 'a) 160° only'.
Given Information:
- Smallest angle of the polygon = 120°
- Common difference between interior angles = 5°
Concept:
- The sum of interior angles of a polygon with n sides is given by the formula (n-2)*180°.
- In an arithmetic progression, the sum of angles is equal to the number of sides multiplied by the average of the first and last angles.
Finding the Largest Angle:
- Let the largest angle be x°.
- Since the smallest angle is 120° and the common difference is 5°, the second smallest angle is 120 + 5 = 125°.
- The average of the first and last angles in an AP is (120 + x)/2.
- The sum of angles of the polygon with n sides is n*(120 + x)/2.
- This sum is also equal to (n-2)*180°.
- Equating the two expressions for the sum of angles, we get: n*(120 + x)/2 = (n-2)*180
- Solving this equation, we get x = 160°.
Conclusion:
- Therefore, the largest interior angle of the polygon is 160°.
- Hence, the correct answer is option 'a) 160° only'.
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Consider the followingThe interior angles of a polygon of n sides are in AP. The smallest angle is 120° and the common difference is 5°.Q. What is the largest interior angle of the polygon?a)160° onlyb)195° onlyc)Either 160° or 195°d)Nither 160 nor 195°Correct answer is option 'A'. Can you explain this answer?
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Consider the followingThe interior angles of a polygon of n sides are in AP. The smallest angle is 120° and the common difference is 5°.Q. What is the largest interior angle of the polygon?a)160° onlyb)195° onlyc)Either 160° or 195°d)Nither 160 nor 195°Correct answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Consider the followingThe interior angles of a polygon of n sides are in AP. The smallest angle is 120° and the common difference is 5°.Q. What is the largest interior angle of the polygon?a)160° onlyb)195° onlyc)Either 160° or 195°d)Nither 160 nor 195°Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the followingThe interior angles of a polygon of n sides are in AP. The smallest angle is 120° and the common difference is 5°.Q. What is the largest interior angle of the polygon?a)160° onlyb)195° onlyc)Either 160° or 195°d)Nither 160 nor 195°Correct answer is option 'A'. Can you explain this answer?.
Solutions for Consider the followingThe interior angles of a polygon of n sides are in AP. The smallest angle is 120° and the common difference is 5°.Q. What is the largest interior angle of the polygon?a)160° onlyb)195° onlyc)Either 160° or 195°d)Nither 160 nor 195°Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Defence.
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