Question

In the given figure $AC\parallel BD$, and $AE\parallel BF$. The measure of $\angle x$ is

• A. ${130}^o$
• B. ${110}^o$
• C. ${70}^o$
• D. ${50}^o$

Answer 1

The correct option is B ${110}^o$

$\angle CAB+\angle DBA={180}^o$
$\angle DBA={180}^o-\angle CAB={180}^o-{130}^o={50}^o$
($AC\parallel BD$, co-int. $\angle s$ are supp.)
$DBG$ being a straight line, $\angle DBG={180}^o$
$\Rightarrow$ $\angle DBA+\angle ABF+\angle FBG={180}^o$
$\Rightarrow$ ${50}^o+\angle ABF+{60}^o={180}^o$
$\Rightarrow$ $\angle ABF={180}^o-{110}^o={70}^o$
Now, $AE\parallel BF$ $\Rightarrow$ $\angle EAB+\angle ABF={180}^o$ (co-int $\angle s$)
$\Rightarrow$ $x+{70}^o={180}^o$

$\Rightarrow x={110}^o$