Question:
In ∆ABC, AB = AC and ∠B = 50°. Then, ∠A = ?
(a) 40°
(b) 50°
(c) 80°
(d) 130°
Solution:
In $\triangle A B C$, we have:
$A B=A C$
$\angle B=50^{\circ}$
Since $A B C$ is an isosceles triangle, we have:
$\angle C=\angle B$
$\angle C=50^{\circ}$
In triangle $\mathrm{ABC}$, we have:
$\angle A+\angle B+\angle C=180^{\circ}$
$\Rightarrow \angle A+50+50=180^{\circ}$
$\Rightarrow \angle A=180^{\circ}-100^{\circ}$
$\therefore \angle A=80^{\circ}$
Hence, the correct answer is option (c).