Question

If ABC is a triangle such that AB = BC and $\angle B={60}^{\circ }$, then what is the $\angle A$?

• A. $\angle A={60}^{\circ }$
  
• B. $\angle A={70}^{\circ }$
  
• C. $\angle A={45}^{\circ }$
  
• D. $\angle A={30}^{\circ }$
  

Answer 1

The correct option is A $\angle A={60}^{\circ }$


Given,
AB = BC
$\angle B={60}^{\circ }$

Now,
$\angle A=\angle C$ .. (i)
[Angles opposite to equal sides are always equal]

In $\Delta$ ABC,
$\angle A+\angle B+\angle C={180}^{\circ }$
[Angle Sum Property]
$2\angle A+{60}^{\circ }={180}^{\circ }$ [From (i)]
$2\angle A={120}^{\circ }$
$\angle A={60}^{\circ }$