Question

Is it possible to have regular polygon with each interior angle equal to 105°...Justify.

Answer 1

Hey there!

We know,

each interiror angle = [(2n - 4) * 90] / n

105 = [180n - 360] / n

105n = 180n - 360

180n - 105n = 360

75n = 360

n = 360 / 75

n = 4.8

Hence, it is not possible for  a polygon to have each interior angle = 105°.

Answer 2

We know,

each interiror angle = [(2n - 4) * 90] / n

108 = [180n - 360] / n

108n = 180n - 360

180n - 108n = 360

72n = 360

n = 360 / 72

n = 5

Hence, it is possible

Step-by-step explanation: