Question

The sum of all the interior angles of a regular polygon is 1260° , then the number of sides and diagonals respectively are​

Answer 1

Answer:

diagonals of polygon is 2 and no of sides are 5

Answer 2

$\blue { The \:sum \:of \:the \: measures \: of }\\\blue { the \: interior \: angles \:of \: a \: polygon}\\\blue {n \:sides } \pink { = (n-2)180\degree }$

$Let \: number \:of \:sides \: of \:a \:polygon= n$

$\implies (n-2) 180 = 1260 \: (given)$

$\implies n -2 = \frac{1260}{180}$

$\implies n - 2 = 7$

$\implies n = 7 + 2$

$\implies n = 9$

$\pink { Number \:of \: diagonals \: in }\\\pink { a \: polygon }= \frac{n(n-3)}{2} \\= \frac{9(9-1)}{2} \\= \frac{9 \times 8}{2} \\= 9 \times 4 \\= 36$

Therefore.,

$\red{number \:of \:sides \: of \:a \:polygon} \green {= 9 }$

$\red{Number \:of \: diagonals }\green {= 36}$

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