Question

Find out if it is possible to have a regular polygon with each interior angle equal to
105°.​

Answer 1

Step-by-step explanation:

total angle of the n-sided regular polygon = 180(n-2).

4- sided regular polygon has each angle=90°

5-sided regular polygon has each angle=108.

108*5=540.

by formula total angle of 5-sided regular polygon=180(5-2)

=180*3

= 540

therefore total angle of 6-sided regular polygon=180(6-2)

=180*4

=720

6-sided regular polygon has the each angle =720/6

=120

therefore ,it is no possible to have a regular polygon with each interior angle equal to

105°.

Answer 2

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°.