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Sum of interior angles must be equal to ______
- a)(2n/4) right angles
- b)(2n*4) right angles
- c)(2n+4) right angles
- d)(2n-4) right angles
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Sum of interior angles must be equal to ______a)(2n/4) right anglesb)(...
The check applied for finding the sum of interior angles is equal to (2n-4) right angles. Similarly, the check for exterior angles is equal to (2n+4) right angles.
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Sum of interior angles must be equal to ______a)(2n/4) right anglesb)(...
Explanation:
The sum of the interior angles of a polygon can be calculated using the formula:
Sum of interior angles = (n - 2) * 180 degrees
where n is the number of sides or vertices of the polygon.
Proof:
To prove that the sum of interior angles is equal to (2n - 4) right angles, we can substitute the value of (n - 2) from the formula into the equation for the sum of interior angles.
Sum of interior angles = (n - 2) * 180 degrees
= (n * 180 degrees) - (2 * 180 degrees)
= (n * 180 degrees) - 360 degrees
We know that 1 right angle is equal to 90 degrees. Therefore, (2n - 4) right angles can be written as (2n - 4) * 90 degrees.
To prove that the two expressions are equal, we can equate them:
(n * 180 degrees) - 360 degrees = (2n - 4) * 90 degrees
Expanding the equation:
180n - 360 = 180n - 360
As we can see, the equation is true, which means that the sum of interior angles is indeed equal to (2n - 4) right angles.
Therefore, the correct answer is option 'D' - (2n - 4) right angles.
Conclusion:
The sum of the interior angles of a polygon is given by the formula (n - 2) * 180 degrees. This can be simplified to (2n - 4) right angles.
The sum of the interior angles of a polygon can be calculated using the formula:
Sum of interior angles = (n - 2) * 180 degrees
where n is the number of sides or vertices of the polygon.
Proof:
To prove that the sum of interior angles is equal to (2n - 4) right angles, we can substitute the value of (n - 2) from the formula into the equation for the sum of interior angles.
Sum of interior angles = (n - 2) * 180 degrees
= (n * 180 degrees) - (2 * 180 degrees)
= (n * 180 degrees) - 360 degrees
We know that 1 right angle is equal to 90 degrees. Therefore, (2n - 4) right angles can be written as (2n - 4) * 90 degrees.
To prove that the two expressions are equal, we can equate them:
(n * 180 degrees) - 360 degrees = (2n - 4) * 90 degrees
Expanding the equation:
180n - 360 = 180n - 360
As we can see, the equation is true, which means that the sum of interior angles is indeed equal to (2n - 4) right angles.
Therefore, the correct answer is option 'D' - (2n - 4) right angles.
Conclusion:
The sum of the interior angles of a polygon is given by the formula (n - 2) * 180 degrees. This can be simplified to (2n - 4) right angles.
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Sum of interior angles must be equal to ______a)(2n/4) right anglesb)(2n*4) right anglesc)(2n+4) right anglesd)(2n-4) right anglesCorrect answer is option 'D'. Can you explain this answer?
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