Question

Given α and β are Supplementary. Show the necessary steps.

If α =3/2β then, what is α = ? and what is β = ?​

Answer 1

`\alpha = 108\degree, \: \beta = 72\degree`

Explanation:

α and β are Supplementary (given)

`\therefore \alpha + \beta = 180\degree.... (1)`

It is given that:

`\alpha= (3)/(2) \beta`

Plugging the value of α in equation (1), we find:

`(3)/(2) \beta + \beta = 180\degree`

`\therefore (3+2)/(2) \beta = 180\degree`

`\therefore (5)/(2) \beta = 180\degree`

`\therefore \beta = 180\degree* (2)/(5)`

`\therefore \beta = 72\degree`

`\implies \alpha= (3)/(2) * 72\degree= 108\degree`

So,

`\alpha = 108\degree, \: \beta = 72\degree`