Sum of interior angles of a polygon of n-1 sides -A- n-1 - 180-B- 2 n-2 - 180-C- n-2 - 180-D- 2 n-4 - 90-

The correct option is A (n 1) × 180° Sum of interior angles of a polygon of (n) sides is (n 2) × 180^∘ ∴ Sum of interior angles of a polygon of (n+1) sides ...

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Byju's Answer

Standard VIII

Mathematics

Deducing a Formula for Sum of Interior Angles of a Polygon

Sum of interi...

Question

Sum of interior angles of a polygon of $(n + 1)$ sides $=$

(2n - 4) × 90°

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(n - 1) × 180°

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(2n - 2) × 180°

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(n - 2) × 180°

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Solution

The correct option is A $(n - 1) \times 180^{\circ}$

We know that
Sum of interior angles of a polygon of $(n)$ sides $= (n - 2) \times 180^{\circ}$

$∴$ Sum of interior angles of a polygon of $(n + 1)$ sides

$= (n + 1 - 2) \times 180^{\circ}$ [Substituting $n = n + 1$ ]

$= (n - 1) \times 180^{\circ}$

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Similar questions

Q. Sum of interior angles of triangle is

180^{o}

, and that for a quadrilateral is

360^{o}

, then sum of interior angles of a polygon having n sides is

Q. The measure of an angle in degrees, grades and radians be D, G and C respectively, then relation between them

\frac{D}{90} = \frac{G}{100} = \frac{2 C}{π}

but

1^{\circ} = {(\frac{180}{π})}^{\circ} ≃ 57^{\circ}, 17^{'}, 44. 8^{''}

and sum of interior angles of a

n

-sided regular polygon is

(2 n - 4) \frac{π}{2}

. On the basis of above information, answer the following questions :Which of the following are correct

Q. Question 43
Which of the following is not true for an exterior angle of a regular polygon with n sides?
a) Each exterior angle

= \frac{360^{\circ}}{n}

b) Exterior angle

= 180^{\circ}

- Interior angle
c)

n = \frac{360^{\circ}}{E x t e r i o r a n g l e}

d) Each exterior angle

= \frac{(n - 2) \times 180^{\circ}}{n}

Q. Each interior angle of a n-sided regular polygon is

162^{\circ}

. FInd the interior angle of another polygon with 2n sides.

Q. The measure of an angle in degrees, grades and radians be D, G and C respectively, then relation between them

\frac{D}{90} = \frac{G}{100} = \frac{2 C}{π}

but

1^{\circ} = {(\frac{180}{π})}^{\circ} ≃ 57^{\circ}, 17^{'}, 44. 8^{''}

and sum of interior angles of a

n

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(2 n - 4) \frac{π}{2}

. On the basis of above information, answer the following questions :The number of sides of two regular polygon are as 5 : 4 and the difference between their angles is

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then the number of sides in the polygons respectively are -

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Sum of interior angles of a polygon of (n+1) sides =

The correct option is A (n−1)×180∘We know thatSum of interior angles of a polygon of (n) sides =(n−2)×180∘ ∴ Sum of interior angles of a polygon of (n+1) sides =(n+1−2)×180∘ [Substituting n=n+1] =(n−1)×180∘

Sum of interior angles of a polygon of $(n + 1)$ sides $=$