Question

Four angles of a polygon are 110 each and the remaining angles are all equal to 170 each. Find the number of sides.

Answer 1

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$let \: the \: number \: of \: sides \: be \: n \:$




$then \: number \: of \: exterior \: angles \: = n$


$sum \: of \: the \: angles \: in \: a \: polygon \: = (n - 2)$




$four \: angles \: are \: 110 \: deg \: and \: the \: reamaining \: angles \: are \: all \: eqal \: to \: 170deg \: eacg$






$the \: sum \: of \: the \: angles = 4 \times 110 + (n - 4)170$




$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 440 + 170n - 680$





$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - 240 + 170n \: deg \:$






$now \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - 240 + 170n = (n - 2)180$







$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - 240 + 170n = 180n - 360$







$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - 240 + 360 = 180n - 170n$








$120 - 10n$







$n = \frac{120}{10} \\ \\ \\ \\ \\ \: \: \: \: n=12$






Therefore,
there are 12sides.


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