Question

Question 7
It is given that $\Delta ABC\cong \Delta FDE$ and AB =5 cm, $\angle B={40}^{\circ }and\angle A={80}^{\circ }$, then which of the following is true?
(A) DF = 5 cm. $\angle F={60}^{\circ }$
(B) DF = 5 cm. $\angle E={60}^{\circ }$
(C) DE = 5 cm. $\angle E={60}^{\circ }$​​​​​​​
(D) DE = 5 cm. $\angle D={60}^{\circ }$​​​​​​​

Answer 1

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

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