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Determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1:5?
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Determine the number of sides of a polygon whose exterior and interior...
Understanding the Ratio of Exterior and Interior Angles of a Polygon
The sum of the exterior angles of any polygon is always 360 degrees. The interior and exterior angles of a polygon are related by the formula: Exterior Angle = 180° - Interior Angle.
Ratio of Exterior and Interior Angles
Given that the exterior and interior angles of the polygon are in the ratio 1:5, we can represent this as follows:
Let the exterior angle be x degrees and the interior angle be 5x degrees.
Relation between Exterior and Interior Angles
Using the formula mentioned earlier:
x = 180° - 5x
Solving for x:
x + 5x = 180°
6x = 180°
x = 30°
Therefore, the exterior angle is 30 degrees, and the interior angle is 150 degrees.
Finding the Number of Sides
To find the number of sides of the polygon, we use the formula for the sum of the interior angles of a polygon:
Sum of interior angles = (n - 2) * 180°
Where n is the number of sides.
Calculating the Number of Sides
Given that each interior angle is 150 degrees:
150n = (n - 2) * 180
150n = 180n - 360
30n = 360
n = 12
Therefore, the polygon has 12 sides.
The sum of the exterior angles of any polygon is always 360 degrees. The interior and exterior angles of a polygon are related by the formula: Exterior Angle = 180° - Interior Angle.
Ratio of Exterior and Interior Angles
Given that the exterior and interior angles of the polygon are in the ratio 1:5, we can represent this as follows:
Let the exterior angle be x degrees and the interior angle be 5x degrees.
Relation between Exterior and Interior Angles
Using the formula mentioned earlier:
x = 180° - 5x
Solving for x:
x + 5x = 180°
6x = 180°
x = 30°
Therefore, the exterior angle is 30 degrees, and the interior angle is 150 degrees.
Finding the Number of Sides
To find the number of sides of the polygon, we use the formula for the sum of the interior angles of a polygon:
Sum of interior angles = (n - 2) * 180°
Where n is the number of sides.
Calculating the Number of Sides
Given that each interior angle is 150 degrees:
150n = (n - 2) * 180
150n = 180n - 360
30n = 360
n = 12
Therefore, the polygon has 12 sides.
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Determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1:5?
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Determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1:5? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1:5? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1:5?.
Determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1:5? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1:5? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1:5?.
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