Question

I NEED HELP ASAP

Answer 1

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.

$\frac{360}{n}$ = value of exterior angle

Where n is number of sides of ploygon

$\frac{360}{n} = 45$

Multiplying n into both sides

$\frac{360}{n} * n = 45 n$

$360 = 45 n$

Now divide 45 in both sides

$\frac{360}{45} = \frac{45n}{n} = n = 8$

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 = $8 * 135 = 1080$

Hence sum of all interior angles would be 1080°. Answer

Hope it will help :)