Question

Question 4
In $\Delta ABC$, if BC =AB and $\angle B={80}^{\circ }$ then $\angle A$ is equal to
(A) ${80}^{\circ }$
(B) ${40}^{\circ }$
(C) ${50}^{\circ }$
(D) ${100}^{\circ }$

Answer 1

Given $\Delta ABC$ such that BC = AB = and $\angle B={80}^{\circ }$
$In\Delta ABCAB=BC\Rightarrow \angle C=\angle A$
[angles opposite to equal sides are equal]
We know that the sum of all the anlges of a trianlge is ${180}^{\circ }$

$\Rightarrow \angle A+\angle B+\angle C={180}^{\circ }\Rightarrow \angle A+{80}^{\circ }+\angle A={180}^{\circ }\Rightarrow 2\angle A={180}^{\circ }\Rightarrow 2\angle A={180}^{\circ }-{80}^{\circ }={100}^{\circ }\Rightarrow \angle A=\frac{{100}^{\circ }}{2}\Rightarrow \angle A={50}^{\circ }$