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beks73 [17]
2 years ago
14

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

Mathematics
1 answer:
user100 [1]2 years ago
7 0

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

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