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If the angles of a pentagon are in the ratio 1 : 3 : 6 : 7 : 10, then the smallest angle is:
- a)30°
- b)32°
- c)27°
- d)20°
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
If the angles of a pentagon are in the ratio 1 : 3 : 6 : 7 : 10, then...
Suppose the angles of a pentagon are
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x°, 3x°, 6x°, 7x°, 10x°
But x° + 3x° + 6x° + 7x° + 10x° = (2x5 -4) x 90°
or 27x° = 6 x 90°
or x = 20°
Most Upvoted Answer
If the angles of a pentagon are in the ratio 1 : 3 : 6 : 7 : 10, then...
Understanding the Problem
To find the smallest angle in a pentagon where the angles are in the ratio 1 : 3 : 6 : 7 : 10, we first need to determine the total sum of the interior angles of a pentagon.
Sum of Interior Angles
- The formula for the sum of the interior angles of a polygon is:
Sum = (n - 2) × 180°
- For a pentagon (n = 5):
Sum = (5 - 2) × 180° = 3 × 180° = 540°
Setting Up the Ratios
- Let the angles be represented as:
Angle 1 = x (smallest angle)
Angle 2 = 3x
Angle 3 = 6x
Angle 4 = 7x
Angle 5 = 10x
- The total sum of the angles can be expressed as:
x + 3x + 6x + 7x + 10x = 540°
- Simplifying this:
27x = 540°
Calculating the Smallest Angle
- Now, solve for x:
x = 540° / 27
x = 20°
Conclusion
- The smallest angle, represented by x, is therefore 20°.
- Thus, the correct answer is option 'D' - 20°.
This systematic breakdown allows us to understand how to approach similar problems regarding angles in polygons.
To find the smallest angle in a pentagon where the angles are in the ratio 1 : 3 : 6 : 7 : 10, we first need to determine the total sum of the interior angles of a pentagon.
Sum of Interior Angles
- The formula for the sum of the interior angles of a polygon is:
Sum = (n - 2) × 180°
- For a pentagon (n = 5):
Sum = (5 - 2) × 180° = 3 × 180° = 540°
Setting Up the Ratios
- Let the angles be represented as:
Angle 1 = x (smallest angle)
Angle 2 = 3x
Angle 3 = 6x
Angle 4 = 7x
Angle 5 = 10x
- The total sum of the angles can be expressed as:
x + 3x + 6x + 7x + 10x = 540°
- Simplifying this:
27x = 540°
Calculating the Smallest Angle
- Now, solve for x:
x = 540° / 27
x = 20°
Conclusion
- The smallest angle, represented by x, is therefore 20°.
- Thus, the correct answer is option 'D' - 20°.
This systematic breakdown allows us to understand how to approach similar problems regarding angles in polygons.
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If the angles of a pentagon are in the ratio 1 : 3 : 6 : 7 : 10, then the smallest angle is:a)30°b)32°c)27°d)20°Correct answer is option 'D'. Can you explain this answer?
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If the angles of a pentagon are in the ratio 1 : 3 : 6 : 7 : 10, then the smallest angle is:a)30°b)32°c)27°d)20°Correct answer is option 'D'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about If the angles of a pentagon are in the ratio 1 : 3 : 6 : 7 : 10, then the smallest angle is:a)30°b)32°c)27°d)20°Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the angles of a pentagon are in the ratio 1 : 3 : 6 : 7 : 10, then the smallest angle is:a)30°b)32°c)27°d)20°Correct answer is option 'D'. Can you explain this answer?.
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