MCQ
In a $\triangle A B C$, if $A B=A C$ and $\angle B=50^{\circ}$, then $\angle A=$
- A$40^{\circ}$
- B$50^{\circ}$
- C$80^{\circ}$
- D$130^{\circ}$
✓
Answer
C. $80^{\circ}$
We have,
$
A B=A C \Rightarrow \angle C=\angle B \Rightarrow \angle C=50^{\circ} \quad \text { [Angles opposite to equal sides are equal] }
$
Thus, we obtain $\angle B=\angle C=50^{\circ}$.$
\therefore \quad \angle A+\angle B+\angle C=180^{\circ} \Rightarrow \angle A+50^{\circ}+50^{\circ}=180^{\circ} \Rightarrow \angle A=80^{\circ}
$
We have,
$
A B=A C \Rightarrow \angle C=\angle B \Rightarrow \angle C=50^{\circ} \quad \text { [Angles opposite to equal sides are equal] }
$
Thus, we obtain $\angle B=\angle C=50^{\circ}$.$
\therefore \quad \angle A+\angle B+\angle C=180^{\circ} \Rightarrow \angle A+50^{\circ}+50^{\circ}=180^{\circ} \Rightarrow \angle A=80^{\circ}
$
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