Question

In $\Delta ABC,\angle B$ and $\angle C$ are in ratio $3:4$ and $\angle A$ is $\frac{3}{7}$ times its exterior angle. Find the interior and exterior $\angle A$.

Answer 1

$\begin{array}{c}\angle A+\angle B+\angle C={180}^o\\ \angle A+\angle B+\frac{3}{4}\angle B={180}^o\\ \mathrm{interior}\angle A+exterior\angle A={360}^o\\ \mathrm{interior}\angle A=\frac{3}{7}extetior\angle A\\ So,\\ \frac{3}{7}extetior\angle A+exterior\angle A={360}^o\\ \frac{10}{7}exterior\angle A={360}^o\\ exterior\angle A=\frac{360\times 7}{10}={252}^o\\ \mathrm{interior}\angle A=\frac{3}{7}\times 252={108}^o\end{array}$