In ∆ABC, BC = AB and ∠B = 80°. Then, ∠A = ?

Question:

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

Solution:

Given: In ABCBC AB and ∠B = 80°. 

In ABC,

As, $A B=B C$

$\Rightarrow \angle A=\angle C$

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

Using angle sum property of a triangle,

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

$\Rightarrow x+80^{\circ}+x=180^{\circ}$

$\Rightarrow 2 x=180^{\circ}-80^{\circ}$

$\Rightarrow 2 x=100^{\circ}$

$\Rightarrow x=\frac{100^{\circ}}{2}$

$\Rightarrow x=50^{\circ}$

$\Rightarrow \angle A=50^{\circ}$

Hence, the correct option is (a).

 

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