It is given that ≅ and AB = 5 cm, = 40^ and = 80^ Then which of t… - Vidyadip

MCQ

It is given that $\triangle\text{ABC} ≅\triangle\text{FDE}$ and $AB = 5\ cm$, $\angle\text{B} = 40^\circ$ 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
$\text{DE} = 5\text{cm}, \ \angle\text{D} = 40^\circ$
C
$\text{DE} = 5\text{cm}, \ \angle\text{E} = 60^\circ$
✓
$\text{DF} = 5\text{cm}, \ \angle\text{E} = 60^\circ$

✓

Answer

Correct option: D.

$\text{DF} = 5\text{cm}, \ \angle\text{E} = 60^\circ$

Given that: In $\triangle\text{ABC}, \ \text{AB} = 5\text{cm},\ \angle\text{B} = 40^\circ$ and $\angle\text{A} = 80^\circ$
Using angles sum property of triangle, we have
$\angle\text{A} + \angle\text{B} + \angle\text{C} = 180^\circ$
$\Rightarrow 80^\circ + 40^\circ + \angle\text{C} = 180^\circ$
$\Rightarrow 120^\circ + \angle\text{C} = 180^\circ$ [$\therefore\ \angle\text{B} = 40^\circ$ and $\angle\text{A} = 80^\circ$]
$\Rightarrow \angle\text{C} = 180^\circ – 120^\circ$
$\Rightarrow \angle\text{C} = 60^\circ$
It is given that $\triangle\text{ABC} ≅\triangle\text{FDE},$ so we have
$AB = FD, BC = DE$ and $\text{AC}=\text{FE}\ \&\ \angle\text{A} = \angle\text{F}, \ \angle\text{B} = \angle\text{D}$ and $\angle\text{C} = \angle\text{E}$
$\Rightarrow AB = FD = 5cm$ and $\angle\text{C} = \angle\text{E} = 60^\circ$

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