Question

I NEED HELP ASAP

each exterior angle angle of a polygon measures 45 degrees.

1. Find the number of sides the polygon has name the polygon.

2. Find the sum of the measures of the polygons interior angles.

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.

`(360)/(n)` = value of exterior angle

Where n is number of sides of ploygon

`(360)/(n) = 45`

Multiplying n into both sides

`(360)/(n) * n = 45 n`

`360 = 45 n`

Now divide 45 in both sides

`(360)/(45) = (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 :)