Question

In the given figure, $AB||CD,\angle ABE={120}^o,\angle ECD={100}^o$ and $\angle BEC=x^o$. Find the value of $x$

Answer 1

Let AB is parallel to FG, then $\angle ABE=\angle BEG={120}^0$

Also, it is given that CD is parallel to AB and we have assumed that AB is parallel to FG, then CD is parallel to FG

Therefore, considerering CD||FG and CE is

$\angle DCE+\angle CEG={180}^0{100}^0+\angle CEG={180}^0\angle CEG={80}^0\angle BEG=\angle BEC+\angle CEG{120}^0=x+{80}^{0}x={40}^0$

Thus, the value of the $\angle BEC=x={40}^0$