Question

the sum of interior angles of a polygon is five times the sum of its exterior angles. find the number of sides in the polygon​

Answer 1

Answer:

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Answer 2

Answer:

$the \: sum \: of \: exterior \: angles \: of \: a \: regular$

$polygon \: is \: 360 \: degree$

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$given ,\: that \: sum \: of \: interior \: angles \: of \: a$

$polygon \: is \: five \: times \: the \: sum \: of \: it \: s$

$exterior \: angles \:$

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$sum \: of \: interior \: angles \: = 5 \times 360 degree$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 1800 \: degree$

But,

$sum \: of \: interior \: angles \: = (n - 2) \times 180$

According to question:

$(n - 2) \times 180 = 1800 \: degree$

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

$(n - 2) = 1800 \div 180$

$(n - 2) = 10 \: \: \:$

$n = 10 + 2$

$n = 12$

Therefore, Number of sides in the polygon are 12...

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