Question

In a triangle ABC, $AB=AC$ and $\angle$B = 30${}^{\circ }$. Then value of $\angle A$ is .

• A. ${20}^{\circ }$
• B. ${30}^{\circ }$
• C. ${40}^{\circ }$
• D. ${50}^{\circ }$

Answer 1

The correct option is C ${40}^{\circ }$

Since AB = AC, the angles opposite these sides will also be equal.

Hence, $\angle B=\angle C$

$\Rightarrow \angle C={30}^{\circ }$
Now using angle sum property
$\angle A+\angle B+\angle C={180}^{\circ }$
$\angle A+{30}^{\circ }+{30}^{\circ }={180}^{\circ }$
$\angle A+{60}^{\circ }={180}^{\circ }$
$\angle A={120}^{\circ }$