Question

In the given figure, $\angle CAE={84}^{\circ }$. If $\angle B:\angle C=3:4,$ then find the value of $\angle B$ and $\angle C$.

Answer 1

Let $\angle B=3x^{\circ }$ and $\angle C=4x^{\circ }$

$3x^{\circ }+4x^{\circ }={84}^{\circ }...$ (exterior angle theorem)

$\therefore 7x={84}^{\circ }$

$x={12}^{\circ }$

$\therefore \angle B=3\left(12\right)={36}^{\circ }$

$\angle C=4\left(12\right)={48}^{\circ }$

Hence $\angle B=36°and\angle C$ = 48°