Alright, lets get started.
If the polygon measures 45 degree exterior angle and we are asked to find number of sides, there is a formula for that.
[tex] \frac{360}{n} [/tex] = value of exterior angle
Where n is number of sides of ploygon
[tex] \frac{360}{n} = 45 [/tex]
Multiplying n into both sides
[tex] \frac{360}{n} * n = 45 n [/tex]
[tex] 360 = 45 n [/tex]
Now divide 45 in both sides
[tex] \frac{360}{45} = \frac{45n}{n} = n = 8 [/tex]
n = 8
Means number of sides of polygon is 8, hence its Octagon. Answer
Now we have given 45 exterior angle hence interior angle would be
180 - 45 = 135°
So, sum of all interior angles would be = number of sides * interior angle
sum of all interior angles would be = [tex] 8 * 135 = 1080 [/tex]
Hence sum of all interior angles would be 1080°. Answer
Hope it will help :)
