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Each interior angle of a n-sides regular polygon measures 135 find the interior angle of another polygon having 3n sides?
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Each interior angle of a n-sides regular polygon measures 135 find the...
Interior Angle of a Regular Polygon
To find the interior angle of a regular polygon with 3n sides, we can use the formula for calculating the interior angle of a regular polygon, which is:
Interior Angle = (n-2) * 180° / n
Given Information
- The interior angle of a n-sided regular polygon is 135°
Finding the Interior Angle of a 3n-sided Polygon
1. Calculate the number of sides in the 3n-sided polygon:
Number of sides = 3n
2. Substitute the number of sides into the formula for the interior angle of a regular polygon:
Interior Angle = (3n - 2) * 180° / 3n
= (540n - 360) / 3n
= 180 - 120/n
3. Since the interior angle of the n-sided polygon is 135°, we can equate the two angles:
135 = 180 - 120/n
4. Solve for n:
120/n = 45
n = 120/45
n = 8/3
5. Substitute the value of n back into the formula for the interior angle of the 3n-sided polygon:
Interior Angle = 180 - 120/(8/3)
= 180 - 45
= 135°
Conclusion
Therefore, the interior angle of a regular polygon with 3n sides is also 135°. This result is consistent with the given information that each interior angle of the n-sided regular polygon measures 135°.
To find the interior angle of a regular polygon with 3n sides, we can use the formula for calculating the interior angle of a regular polygon, which is:
Interior Angle = (n-2) * 180° / n
Given Information
- The interior angle of a n-sided regular polygon is 135°
Finding the Interior Angle of a 3n-sided Polygon
1. Calculate the number of sides in the 3n-sided polygon:
Number of sides = 3n
2. Substitute the number of sides into the formula for the interior angle of a regular polygon:
Interior Angle = (3n - 2) * 180° / 3n
= (540n - 360) / 3n
= 180 - 120/n
3. Since the interior angle of the n-sided polygon is 135°, we can equate the two angles:
135 = 180 - 120/n
4. Solve for n:
120/n = 45
n = 120/45
n = 8/3
5. Substitute the value of n back into the formula for the interior angle of the 3n-sided polygon:
Interior Angle = 180 - 120/(8/3)
= 180 - 45
= 135°
Conclusion
Therefore, the interior angle of a regular polygon with 3n sides is also 135°. This result is consistent with the given information that each interior angle of the n-sided regular polygon measures 135°.
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Each interior angle of a n-sides regular polygon measures 135 find the interior angle of another polygon having 3n sides?
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Each interior angle of a n-sides regular polygon measures 135 find the interior angle of another polygon having 3n sides? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Each interior angle of a n-sides regular polygon measures 135 find the interior angle of another polygon having 3n sides? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Each interior angle of a n-sides regular polygon measures 135 find the interior angle of another polygon having 3n sides?.
Each interior angle of a n-sides regular polygon measures 135 find the interior angle of another polygon having 3n sides? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Each interior angle of a n-sides regular polygon measures 135 find the interior angle of another polygon having 3n sides? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Each interior angle of a n-sides regular polygon measures 135 find the interior angle of another polygon having 3n sides?.
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