Question

find the number of polygon if the sum of interior angle is ​

Answer 1

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

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$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

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• a) Sum of interior angles is 10 right angles

• b) Sum of interior angles is 720°

• c) Sum of interior angles is 1620°

• d) Sum of interior angles is 540°

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$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

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• The number of sides of polygon in each case

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$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

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We know that the the sum of interior angles of a polygon can be calculated by -

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➠ S = (n - 2) × 180° ⚊⚊⚊⚊ ⓵

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Where ,

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• S = Sum of all interior angles of the polygon

• n = Number of sides of the polygon

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For (a)

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➠ a) 10 right angles

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We know that 1 right angle is of 90°

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Thus ,

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10 right angles = (90 × 10)°

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10 right angles = 900°

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• S = 900°

• n = n

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⟮ Putting the above values in ⓵ ⟯

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: ➜ S = (n - 2) × 180°

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: ➜ 900 = (n - 2) × 180°

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: ➜ $\sf \dfrac { 900 } { 180 } = n - 2$

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: ➜ n - 2 = 5

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: ➜ n = 5 + 2

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: : ➨ n = 7

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• Hence the number of sides in a) is 7

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For (b)

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➠ b) 720°

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• S = 720°

• n = n

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⟮ Putting the above values in ⓵ ⟯

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: ➜ S = (n - 2) × 180°

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: ➜ 720 = (n - 2) × 180

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: ➜ $\sf \dfrac { 720} { 180 } = n - 2$

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: ➜ n - 2 = 4

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: ➜ n = 4 + 2

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: : ➨ n = 6

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• Hence the number of sides in b) is 6

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For (c)

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➠ c) 1620°

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• S = 1620°

• n = n

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⟮ Putting the above values in ⓵ ⟯

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: ➜ S = (n - 2) × 180°

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: ➜ 1620 = (n - 2) × 180

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: ➜ $\sf \dfrac { 1620} { 180 } = n - 2$

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: ➜ n - 2 = 9

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: ➜ n = 9 + 2

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: : ➨ n = 11

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• Hence the number of sides in c) is 11

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For (d)

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➠ d) 540°

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• S = 540°

• n = n

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⟮ Putting the above values in ⓵ ⟯

$\:\:$

: ➜ S = (n - 2) × 180°

$\:\:$

: ➜ 540 = (n - 2) × 180

$\:\:$

: ➜ $\sf \dfrac { 540} { 180 } = n - 2$

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: ➜ n - 2 = 3

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: ➜ n = 3 + 2

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: : ➨ n = 5

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• Hence the number of sides in d) is 5

Answer 2

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

$\:\:$

a) Sum of interior angles is 10 right angles

b) Sum of interior angles is 720°

c) Sum of interior angles is 1620°

d) Sum of interior angles is 540°

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

$\:\:$

• The number of sides of polygon in each case

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

$\:\:$

We know that the the sum of interior angles of a polygon can be calculated by -

$\:\:$

➠ S = (n - 2) × 180° ⚊⚊⚊⚊ ⓵

$\:\:$

Where ,

$\:\:$

S = Sum of all interior angles of the polygon

n = Number of sides of the polygon

$\:\:$

For (a)

$\:\:$

➠ a) 10 right angles

$\:\:$

We know that 1 right angle is of 90°

$\:\:$

Thus ,

$\:\:$

10 right angles = (90 × 10)°

$\:\:$

10 right angles = 900°

$\:\:$

S = 900°

n = n

$\:\:$

⟮ Putting the above values in ⓵ ⟯

$\:\:$

: ➜ S = (n - 2) × 180°

$\:\:$

: ➜ 900 = (n - 2) × 180°

$\:\:$

: ➜ $\sf \dfrac { 900 } { 180 } = n - 2$

$\:\:$

: ➜ n - 2 = 5

$\:\:$

: ➜ n = 5 + 2

$\:\:$

: : ➨ n = 7

$\:\:$

Hence the number of sides in a) is 7

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For (b)

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➠ b) 720°

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S = 720°

n = n

$\:\:$

⟮ Putting the above values in ⓵ ⟯

$\:\:$

: ➜ S = (n - 2) × 180°

$\:\:$

: ➜ 720 = (n - 2) × 180

$\:\:$

: ➜ $\sf \dfrac { 720} { 180 } = n - 2$

$\:\:$

: ➜ n - 2 = 4

$\:\:$

: ➜ n = 4 + 2

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: : ➨ n = 6

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Hence the number of sides in b) is 6

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For (c)

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➠ c) 1620°

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S = 1620°

n = n

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⟮ Putting the above values in ⓵ ⟯

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: ➜ S = (n - 2) × 180°

$\:\:$

: ➜ 1620 = (n - 2) × 180

$\:\:$

: ➜ $\sf \dfrac { 1620} { 180 } = n - 2$

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: ➜ n - 2 = 9

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: ➜ n = 9 + 2

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: : ➨ n = 11

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Hence the number of sides in c) is 11

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For (d)

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➠ d) 540°

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S = 540°

n = n

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⟮ Putting the above values in ⓵ ⟯

$\:\:$

: ➜ S = (n - 2) × 180°

$\:\:$

: ➜ 540 = (n - 2) × 180

$\:\:$

: ➜ $\sf \dfrac { 540} { 180 } = n - 2$

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: ➜ n - 2 = 3

$\:\:$

: ➜ n = 3 + 2

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: : ➨ n = 5

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Hence the number of sides in d) is 5