Question

In ∆ABC, BC = AB and ∠B = 80°. Then, ∠A = ?
(a) 50°
(b) 40°
(c) 100°
(d) 80°

Answer 1

Given: In ∆ABC, BC = AB and ∠B = 80°.

In ∆ABC,

As, $AB=BC$

$\Rightarrow \angle A=\angle C$

Let $\angle A=\angle C=x$

Using angle sum property of a triangle,

$$\begin{gathered} \angle A+\angle B+\angle C=180° \\ \Rightarrow x+80°+x=180° \\ \Rightarrow 2x=180°-80° \\ \Rightarrow 2x=100° \end{gathered}$$

$$\begin{gathered} \Rightarrow x=\frac{100°}{2} \\ \Rightarrow x=50° \\ \Rightarrow \angle A=50° \end{gathered}$$

Hence, the correct option is (a).