Question

Question 92

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

Answer 1

AF and ED are parallel and EF is transveral.
Then, $\angle AFE=\angle FED\left[alternateinteriorangles\right]\Rightarrow AFE={42}^{\circ }[\therefore \angle FED={42}^{\circ }]$
Now, $\angle AFC+\angle AFE+\angle EFD={180}^{\circ }[\therefore Sumofallanglesonastraightlineis{180}^{\circ }]\Rightarrow {68}^{\circ }+{42}^{\circ }+\angle EFD={180}^{\circ }\Rightarrow {110}^{\circ }+\angle EFD=180\Rightarrow \angle EFD={180}^{\circ }-{110}^{\circ }={70}^{\circ }$