Question

In a $\Delta ABC,if\angle A={120}^{\circ }andAB=AC.Find\angle Band\angle C.$

Answer 1

In $\Delta ABC,\angle A={120}^{\circ }andAB=AC.$

$\therefore \angle B=\angle C$ (Angles opposite to equal sides)

But $\angle A+\angle B+\angle C={180}^{\circ }$

(Sum of angles of a triangle)

$\Rightarrow {120}^{\circ }+\angle B+\angle B={180}^{\circ }$

$\Rightarrow 2\angle B={180}^{\circ }-{120}^{\circ }={60}^{\circ }$

$\therefore \angle B=\frac{{60}^{\circ }}{2}={30}^{\circ }$

and $\angle C=\angle B={30}^{\circ }$

Hence $\angle B={30}^{\circ }and\angle C={30}^{\circ }$