Question

The measure of each interior angle of a

regular polygon is 135°. How many sides does the polygon have?
A. 5
B. 6
C. 7
D. 8
E. Cannot be determined from the
information given.

Answer 1

8 sides

Explanation:

Let n be the number of sides

Then sum of internal angles
`=(n-2)180`

——-(1)

It is given that one internal angle
`=135`

So sum of n equal internal angles
`=135n` ————(2)

From(1) and(2)

`(n-2)180=135n`

`180n-360=135n`

`180n-135n=360`

`45n=360`

`n=360/45=8`

`\bold{So \ the \ number \ of \ sides=8}`