Question

In the given figure,$AB||CD.$ Find the reflex $\angle EFG.$

Answer 1

Construct a line l parallel to AB passing through F. l is parallel to both AB and CD. Then,
$\angle 1={34}^{\circ }$ ( alternate angles)
$\angle 2+{135}^{\circ }={180}^{\circ }$ (consecutive angles)
$\Rightarrow \angle 2={180}^{\circ }-{135}^{\circ }$
$\Rightarrow \angle 2={45}^{\circ }$
$\therefore \angle EFG=\angle 1+\angle 2$
$\Rightarrow EFG={34}^{\circ }+{45}^{\circ }$
$\Rightarrow \angle EFG={79}^{\circ }$
$\therefore \text{Reflex of}\angle EFG={360}^{\circ }-\angle EFG$
= ${360}^{\circ }-{79}^{\circ }$
= ${281}^{\circ }$