It is given that in which AB = 5cm, =40^ , =80^ and FD = 5cm. The… - Vidyadip

Question

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

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Answer

$\angle\text{E}=60^{\circ}$
Solution:
Given $\triangle\text{ABC}\cong\triangle\text{FDE}$
$\angle\text{A}=\angle\text{F}=80^{\circ}$ ...(C.P.C.T.)
$\angle\text{B}=\angle\text{D}=40^{\circ}$ ...(C.P.C.T.)
$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^{\circ}$ ...(Angle sum property)
$\Rightarrow80^{\circ}+40^{\circ}+\angle\text{C}=180^{\circ}$
$\Rightarrow\angle\text{C}=60^{\circ}$
$\therefore\angle\text{E}=\angle\text{C}=60^{\circ}$
$\therefore\angle\text{E}=60^{\circ}$

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