Question

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

Answer 1

Answer:

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

Step-by-step explanation:

α and β are Supplementary (given)

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

It is given that:

$\alpha= \frac{3}{2} \beta$

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

$\frac{3}{2} \beta + \beta = 180\degree$

$\therefore \frac{3+2}{2} \beta = 180\degree$

$\therefore \frac{5}{2} \beta = 180\degree$

$\therefore \beta = 180\degree\times \frac{2}{5}$

$\therefore \beta = 72\degree$

$\implies \alpha= \frac{3}{2} \times 72\degree= 108\degree$

So,

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