Question

Question 106

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,
$\angle 1={34}^{\circ }\left[alternateangles\right]and\angle 2+{135}^{\circ }={180}^{\circ }\left[consecutiveangles\right]\Rightarrow \angle 2={180}^{\circ }-{135}^{\circ }\Rightarrow \angle 2={45}^{\circ }\therefore \angle EFG=\angle 1+\angle 2\Rightarrow EFG={34}^{\circ }+{45}^{\circ }\Rightarrow \angle EFG={79}^{\circ }\therefore Reflexof\angle EFG={360}^{\circ }-\angle EFG={360}^{\circ }-{79}^{\circ }={281}^{\circ }$