Question

A polygon is such that one of its exterior angle is 60°,two other are(90-m)° each,while the remaining angles are(30+2m)°each.Find the value of m?

Answer 1

If we know the number of sides then we can work it out.

Explanation:

Exterior angles total `360^@`

We have

`60+(90-m) +(90-m)+(30+2m)+?=360`

If we add these up

`270+0m=360`

so we are `90^@` short

If we add another `(30+2m) => 30+2m=90 => m=30`

if we add 2 more angles `60+4m=90 => m=7.5`

if we add 3 more angles `90+6m=90 => m=0`

if we add 4 more angles `120+8m=90 => m=-3.75`