Question

how many sides does a regular polygon have if each of its interior angle is 156 degree

Answer 1

Hi friend!

$<b>Q: How many sides does a regular polygon have if each of its interior angles is 156°</b>$

$<big><b><u>Answer:</u></b></big>$
Given that:
$Type of polygon: Regular (Equi<i>angular</i>)$
Each interior angle: 156°

Each exterior angle = 180° - 156° = 24° (Linear pair)
Sum of all exterior angles = 360°
No. of sides = n

$No. \: of \: sides = \frac{Sum \: of \: all \: exterior \: angles}{Each \: exterior \: angle} \\ n = \frac{s}{e} \\ \\ n = \frac{360°}{24°} \\ \\ n = 15$

No. of sides = n = 15
$Therefore, the polygon has <b>15 sides</b>.$

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Answer 2

measure of the each interior angles of regular polygon = (n -2)×180/ n

where "n" is the number of sides of regular polygon .
so now,

(n - 2)180 / n= 156

180n - 360 = 156n

180n - 156n = 360

24n = 360

n = 360 / 24 = 15

n= 15

hence the number of sides will be = 15

note : - this formula can be used to find the measure of each interior angles of regular polygon if you have given number of sides.

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