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
    $\text{DE}=5\text{cm},\angle\text{E}=60^\circ$
  • $\text{DF}=5\text{cm},\angle\text{E}=60^\circ$
  • D
    $\text{DE}=5\text{cm},\angle\text{D}=40^\circ$

Answer

Correct option: C.
$\text{DF}=5\text{cm},\angle\text{E}=60^\circ$
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 $(c).$

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