Question

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

The correct option is C ${50}^{\circ }$

Given, in $\Delta ABC$, BC = AB and $\angle B={80}^{\circ }$.
$\Rightarrow \angle C=\angle A$
[angles opposite to equal sides of a triangle are equal]
We know that the sum of all the angles of a triangle is ${180}^{\circ }$.
$\Rightarrow \angle A+\angle B+\angle C={180}^{\circ }\Rightarrow \angle A+{80}^{\circ }+\angle A={180}^{\circ }\Rightarrow 2\angle A={100}^{\circ }\Rightarrow \angle A=\frac{{100}^{\circ }}{2}\therefore \angle A={50}^{\circ }$