Question

In figure, prove that $AB||EF$.

Answer 1

$\begin{array}{c}\angle COE+\angle OEC+\angle OCE={180}^{\circ }\\ \angle COE+{35}^{\circ }+{30}^{\circ }={180}^{\circ }\\ \angle COE={115}^{\circ }\\ \angle BOE={180}^{\circ }-{115}^{\circ }\\ \angle BOE={65}^{\circ }\\ \therefore \angle ABO=\angle BOE\\ \Rightarrow AB\parallel EF\\ \left[alternateanglesareequal\right]\end{array}$