Question

It is given that $\Delta ABC\cong \Delta FDE$ and AB = 5 cm, $\angle B={40}^{\circ }\text{and}\angle A={80}^{\circ }$, then which of the following is true?

• A. DF = 5 cm and $\angle F={60}^{\circ }$
• B. DF = 5 cm and $\angle E={60}^{\circ }$
• C. DE = 5 cm and $\angle E={60}^{\circ }$​​​​​​
• D. DE = 5 cm and $\angle D={60}^{\circ }$

Answer 1

The correct option is B DF = 5 cm and $\angle E={60}^{\circ }$

Given,
$\Delta ABC\cong \Delta FDE$,
AB =5 cm, $\angle B={40}^{\circ }$ and $\angle A={80}^{\circ }$.


$⟹$DF = AB [by CPCT]
$\therefore$ DF = 5 cm
Also, $\angle E=\angle C$ [by CPCT]
$\angle E=\angle C={180}^{\circ }-(\angle A+\angle B)$
$⟹\angle E={180}^{\circ }-({80}^{\circ }+{40}^{\circ })$
$⟹\angle E={60}^{\circ }$