Question

Referring the figure below, for $\Delta ABC$ and $\Delta DEF$, $AB=DE,BC=EF$ and

$\angle B=\angle E.$ The value of $\angle E$ is .........

• A. ${30}^o$
• B. ${60}^o$
• C. ${90}^o$
• D. ${45}^o$

Answer 1

The correct option is B ${60}^o$

For $\Delta ABC$ and $\Delta DEF$
$AB=DE,BC=EF$ and $\angle B=\angle E$
$\therefore \Delta ABC\cong \Delta DEF$ (S.A.S condition for congruence)
As, $AB=DE\Rightarrow \angle C=\angle F={60}^o$
$BC=EF\Rightarrow \angle A=\angle D={60}^o$
$AC=DF\Rightarrow \angle B=\angle E$
Now, $\angle D+\angle E+\angle F={180}^o$
$\therefore {120}^o+\angle E={180}^o$
$\therefore \angle E={60}^o$