Question

In the figure given below, $AB||CD,AF||ED,\angle AFC={68}^{\circ }and\angle FED={42}^{\circ }$.
Find the value of $\angle EFD$.

• A. ${170}^{\circ }$
• B. ${50}^{\circ }$
• C. ${70}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is C ${70}^{\circ }$

Since AF||ED and EF is a transversal.
$\therefore \angle DEF=\angle EFA$ (Alternate interior angles are equal)
Or, ${42}^{\circ }=\angle EFA$
Now CFD make a straight line.
$\therefore \angle AFC+\angle EFA+\angle EFD={180}^{\circ }$
Or $68+{42}^{\circ }+\angle EFD={180}^{\circ }$
Or $\angle EFD={180}^{\circ }-{68}^{\circ }-{42}^{\circ }$
$={180}^{\circ }-{110}^{\circ }$
$={70}^{\circ }$