Question

In fig. 2, lines $l_1||l_2$. The value of $x$ is :

• A. ${70}^{\circ }$
• B. ${30}^{\circ }$
• C. ${40}^{\circ }$
• D. ${50}^{\circ }$

Answer 1

Answer: (B)

${30}^{\circ }$

Here $l_1||l_2$ and $AC$ is transversal.

$\therefore \angle FAB=\angle EBC$ (corresponding angles)

$\Rightarrow \angle EBC={70}^{\circ }$

We know exterior angle of any triangle is equal to the sum of interior opposite angles.

Applying the same in $△DBC$

$\Rightarrow \angle BCD+\angle BDC=\angle EBC$

$\Rightarrow x+{40}^{\circ }={70}^{\circ }\Rightarrow x={70}^{\circ }-{40}^{\circ }={30}^{\circ }$