Question
In the given figure, AB || CD, $\angle\text{ABE}=120^\circ,\ \angle\text{ECD}=100^\circ$ and $\angle\text{BEC}=\text{x}^\circ.$ Find the value of x.
✓
Answer
Given: AB || CD$\angle\text{ABE}=120^\circ$$\angle\text{ECD}=100^\circ$
$\angle\text{BEC}=\text{X}^\circ$
Construction: FEG || AB Now, sin ce AB || FEG and AB || CD, FEG || CD$\therefore\ \text{EFG || AB || CD}$
$\angle\text{ABE}=\angle\text{BEG}=120^\circ$ (alternate angles)
$\text{x}^\circ+\text{y}^\circ=120^\circ\ ....\text{(i)}$
$\angle\text{DCE}=\angle\text{CEF}=100^\circ$ (alternate angles)
$\text{x}^\circ+\text{z}^\circ=100^\circ\ ....\text{(ii)}$
Also, $\text{x}^\circ+\text{y}^\circ+\text{z}^\circ=180^\circ$ (FEG is a s traight line) ....(iii)$2\text{x}^\circ+\text{y}^\circ+\text{z}^\circ=220^\circ$
$\text{x}^\circ+108^\circ=220^\circ$ (substituting (iii))
$\therefore\ \text{x}^\circ=40$
$\therefore\ \text{x}=40$
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