Question

If $\Delta ABC$ is a triangle such that AB = BC and $\angle B={120}^{\circ }$, then what are the other pair of angles?

• A. ${30}^{\circ },{30}^{\circ }$
• B. ${60}^{\circ },{30}^{\circ }$
• C. ${45}^{\circ },{30}^{\circ }$
• D. ${50}^{\circ },{30}^{\circ }$

Answer 1

The correct option is A ${30}^{\circ },{30}^{\circ }$

Given,
In $\Delta ABC$
AB = BC
$\angle B={120}^{\circ }$
$\angle A=\angle C$ ..(i)
[Angles opposite to equal sides are equal]

Now,
$\angle A+\angle B+\angle C={180}^{\circ }$
$\angle A+{120}^{\circ }+\angle A={180}^{\circ }$ ..[from (i)]
$2\angle A+{120}^{\circ }={180}^{\circ }$
$2\angle A={60}^{\circ }$
$\angle A={30}^{\circ }$
$\angle C={30}^{\circ }$
Tha pair of angles are ${30}^{\circ },{30}^{\circ }$