Find the number of sides of a regular polygon, when each of its angles has a measure: `160^@` (ii) `135^@` (iii) `175^@` `162^@` (v) `150^@`

Explanation

We can find the sides of polygon by using the formula:
`n(180^@-A)=360^@`
Where, `n` is number of sides and `A` is the angle given.
(i)`160^@`
`A=160^@`
`n(180^@-160^@)=360^@`
`n(20^@)=360^@`
`n=360^@/20^@`
`n=18`

(ii)`135^@`
`A=135^@`
`n(180^@-135^@)=360^@`
`n(45^@)=360^@`
`n=360^@/45^@`
`n=8`

(iii)`175^@`
`A=175^@`
`n(180^@-175^@)=360^@`
`n(5^@)=360^@`
`n=360^@/5^@`
`n=72`

(iv)`162^@`
`A=162^@`
`n(180^@-162^@)=360^@`
`n(18^@)=360^@`
`n=360^@/18^@`
`n=20`

(v)`150^@`
`A=150^@`
`n(180^@-150^@)=360^@`
`n(30^@)=360^@`
`n=360^@/30^@`
`n=12`