In a $\triangle ABC, \angle C = 3 \angle B = 2(\angle A + \angle B)$. Find the three angles.
Given:
In a $\triangle ABC, \angle C = 3 \angle B = 2(\angle A + \angle B)$.
To do:
We have to find the three angles.
Solution:
We know that,
The sum of the angles in a triangle is $180^o$
This implies,
$\angle A+\angle B+\angle C=180$......(i)
$\angle C=3 \angle B=2(\angle A+\angle B$
$3 \angle B=2(\angle A+\angle B)$
$2 \angle A=3 \angle B-2 \angle B$
$2 \angle A=\angle B$
$\angle A=\frac{\angle B}{2}$
Substitute the above in (i),
$\frac{\angle B}{2}+\angle B+3 \angle B=180^o$
$\frac{\angle B}{2}+4 \angle B=180^o$
$\angle B(\frac{1+8}{2})=180^o$
$\angle B \times \frac{9}{2}=180^o$
$\angle B=\frac{180^o\times2}{9}=40^o$
\end{array}
This implies,
$\angle C=3(40^o)=120^o$
$\angle A=\frac{40^o}{2}=20^o$
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