Question

Given: line BC is parallel to line ED
m∠ABC = 70°
m∠CED = 30°

Prove: m∠BEC = 40°

Answer 1

The Solution.

It is given that

$\begin{gathered} m\angle ABC=70^o \\ m\angle CED=30^o \end{gathered}$

By alternate angles,

$m\angle BED=m\angle ABC=70^o\text{ (Alternate angles)}$

But

$m\angle BED=m\angle BEC+m\angle\text{CED}$

So,

$70=m\angle BEC+30$$m\angle BEC=70-30=40^o$

Hence, the correct answer is 40 degrees.