If ABC and DEF are two triangles such that and AB=5m, =40^ and =80^ . Then, which of the following is true?

If ABC and DEF are two triangles such that and AB=5m, =40^ and =8…

MCQ

If ABC and DEF are two triangles such that $\triangle\text{ABC}\cong\triangle\text{FDE}$ and $\text{AB}=5\text{m},\angle\text{B}=40^\circ$ and $\angle\text{A}=80^\circ.$ Then, which of the following is true?

A
$\text{DF}=5\text{cm},\angle\text{F}=60^\circ$
B
$\text{DE}=5\text{cm},\angle\text{E}=60^\circ$
C
$\text{DF}=5\text{cm},\angle\text{E}=60^\circ$
D
$\text{DE}=5\text{cm},\angle\text{D}=40^\circ$

✓

Answer

$\text{DF}=5\text{cm},\angle\text{E}=60^\circ$
Solution:
In $\triangle\text{ABC},$
$\angle\text{C}=180^\circ-\angle\text{A}+\angle\text{B}=180^\circ-80^\circ-40^\circ=60^\circ$
$\triangle\text{ABC}\cong\triangle\text{FDE}$
$\Rightarrow\text{AB}=\text{FD}=5\text{cm}$
$\Rightarrow\angle\text{B}=\angle\text{D}=40^\circ$
$\Rightarrow\angle\text{A}=\angle\text{F}=80^\circ$
$\Rightarrow\angle\text{C}=\angle\text{E}=60^\circ$
$\Rightarrow\text{DF}=\text{FD}=5\text{cm}$ and $\angle\text{E}=60^\circ$
Hence, correct option is (c).