Question:
It is given that ∆ABC ≅ ∆ FDE in which AB = 5 cm, ∠B = 40°, ∠A = 80° and FD = 5 cm. Then, which of the following is true?
(a) ∠D = 60°
(b) ∠E = 60°
(c) ∠F = 60°
(d) ∠D = 80°
Solution:
(b) $\angle E=60^{\circ}$
$\Delta A B C \cong \Delta F D E$
$\mathrm{AB}=5 \mathrm{~cm}, \angle B=40^{\circ}, \angle A=80^{\circ}$ and $\mathrm{FD}=5 \mathrm{~cm}$
Then $\angle A+\angle B+\angle C=180^{\circ}$
$\Rightarrow 80^{\circ}+40^{\circ}+\angle C=180^{\circ}$
$\Rightarrow \angle C=60^{\circ}$
Also, $\angle C=\angle E$
$\therefore \angle E=60^{\circ}$
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