Question

For the given isosceles triangle find the angle $\angle B.$

• A. ${60}^o$
• B. ${59}^o$
• C. ${58}^o$
• D. ${57}^o$

Answer 1

The correct option is B ${59}^o$

For the given triangle, AC = BC.
$\therefore$ The opposite angles are equal.
$\Rightarrow \angle A=\angle B$


The given ${118}^o$ is the exterior angle at C.
$\therefore \angle ACB={180}^o-{118}^o={62}^o$

We know sum of inerior angles $={180}^o$
$\Rightarrow \angle A+\angle B+\angle C={180}^o$
$\Rightarrow 2\angle B+{62}^o={180}^o$
$\Rightarrow \angle B=\frac{{180}^o-{62}^o}{2}=\frac{{118}^o}{2}={59}^o$