In the given figure, find F. - Vidyadip

MCQ

In the given figure, find $\angle F$.

✓
$60^{\circ}$
B
$80^{\circ}$
C
$40^{\circ}$
D
$100^{\circ}$

✓

Answer

Correct option: A.

$60^{\circ}$

In triangles $\text{ABC}$ and $\text{DFE}$, we have
$\frac{AB}{DF}=\frac{3.8}{7.6}=\frac{1}{2}, \frac{BC}{FE}=\frac{6}{12}=\frac{1}{2}, \frac{CA}{ED}=\frac{3 \sqrt{3}}{6 \sqrt{3}}=\frac{1}{2}$
$\therefore \triangle \text{ABC} \sim \triangle \text{DFE} ($By $\text{SSS}$ similarity criterion $)$
$\Rightarrow \angle A=\angle D, \angle B=\angle F$ and $\angle C=\angle E$
$($Corresponding angles of similar triangles$)$
Hence, $\angle F=60^{\circ}$

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