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The exterior angle of a regular polygon is one third of its interior angle.find the no. Of side in a polygon?
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The exterior angle of a regular polygon is one third of its interior a...
Understanding the Problem:
The problem states that the exterior angle of a regular polygon is one third of its interior angle. We need to find the number of sides in this polygon.
Solution:
To solve this problem, we need to understand the relationship between the exterior angle and the interior angle of a regular polygon.
Relationship between Exterior and Interior Angles:
- The sum of an exterior angle and an interior angle of a regular polygon is always 180 degrees.
- Let x be the interior angle of the polygon. Therefore, the exterior angle will be x/3.
Setting up the Equation:
- According to the relationship between exterior and interior angles, we can write the equation: x + x/3 = 180
- Simplifying the equation gives us: 4x/3 = 180
- Solving for x, we find that x = 135 degrees.
Calculating the Number of Sides:
- In a regular polygon, the interior angle can be calculated using the formula: (n-2) * 180 / n = x, where n is the number of sides.
- Substituting the value of x as 135 degrees, we get: (n-2) * 180 / n = 135
- Solving this equation, we find that n = 8.
Therefore, the number of sides in the polygon is 8.
The problem states that the exterior angle of a regular polygon is one third of its interior angle. We need to find the number of sides in this polygon.
Solution:
To solve this problem, we need to understand the relationship between the exterior angle and the interior angle of a regular polygon.
Relationship between Exterior and Interior Angles:
- The sum of an exterior angle and an interior angle of a regular polygon is always 180 degrees.
- Let x be the interior angle of the polygon. Therefore, the exterior angle will be x/3.
Setting up the Equation:
- According to the relationship between exterior and interior angles, we can write the equation: x + x/3 = 180
- Simplifying the equation gives us: 4x/3 = 180
- Solving for x, we find that x = 135 degrees.
Calculating the Number of Sides:
- In a regular polygon, the interior angle can be calculated using the formula: (n-2) * 180 / n = x, where n is the number of sides.
- Substituting the value of x as 135 degrees, we get: (n-2) * 180 / n = 135
- Solving this equation, we find that n = 8.
Therefore, the number of sides in the polygon is 8.
Community Answer
The exterior angle of a regular polygon is one third of its interior a...
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The exterior angle of a regular polygon is one third of its interior angle.find the no. Of side in a polygon?
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The exterior angle of a regular polygon is one third of its interior angle.find the no. Of side in a polygon? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The exterior angle of a regular polygon is one third of its interior angle.find the no. Of side in a polygon? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The exterior angle of a regular polygon is one third of its interior angle.find the no. Of side in a polygon?.
The exterior angle of a regular polygon is one third of its interior angle.find the no. Of side in a polygon? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The exterior angle of a regular polygon is one third of its interior angle.find the no. Of side in a polygon? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The exterior angle of a regular polygon is one third of its interior angle.find the no. Of side in a polygon?.
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