Question

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

• A.
  $AngleF={70}^{\circ }$
• B.
  $AngleF={60}^{\circ }$
• C.
  $AngleF={80}^{\circ }$
• D.
  $AngleF={50}^{\circ }$

Answer 1

The correct option is A

$AngleF={70}^{\circ }$
$In\Delta ABCand\Delta DEF,\frac{AC}{DE}=\frac{3\sqrt{3}}{6\sqrt{3}}=\frac{1}{2},\frac{AB}{DF}=\frac{38}{76}=\frac{1}{2}\frac{BC}{EF}=\frac{6}{12}=\frac{1}{2}$



$C\to E,B\to F,A\to D\Delta ABC\sim \Delta DFE\text{(By SSS similarity)}\angle B=\angle F\therefore \angle F={70}^{\circ }$