Question

In an isosceles triangle ABC, AB = AC and BA is produced to D, such that AB = AD. What is the value of $\angle BCD$?

• A. ${70}^{\circ }$
• B. ${90}^{\circ }$
• C. ${60}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is B ${90}^{\circ }$

Given, AB = AC and AD = AB
$\Rightarrow AC=AD$
Now, as we know that angles opposite to equal sides are equal. Thus let, $\angle ABC=\angle ACB=x$
and, $\angle ADC=\angle ACD=y$


$\text{Now, in}△BCD$
$x+y+x+y={180}^o$ (Angle sum property)
$\Rightarrow 2x+2y={180}^o$
$\Rightarrow x+y={90}^o$
$\Rightarrow \angle BCD={90}^o$