Question

If $CE$ is parallel to $BD$ in the given figure, then the value of $x$ will be

• A. ${45}^{\circ }$
• B. ${75}^{\circ }$
• C. ${30}^{\circ }$
• D. ${85}^{\circ }$

Answer 1

The correct option is D ${85}^{\circ }$

In $\Delta ADB$,
$\angle ADB+\angle DAB+\angle ABD={180}^{\circ }$
$\Rightarrow \angle ADB+{110}^{\circ }+{30}^{\circ }={180}^{\circ }$
$\Rightarrow \angle ADB={180}^{\circ }-{140}^{\circ }={40}^{\circ }$
$\therefore \angle BDC={75}^{\circ }-\angle ADB={75}^{\circ }-{40}^{\circ }={35}^{\circ }$
In $\Delta BDC$,
$\angle DBC={180}^{\circ }-(\angle BDC+\angle BCD)$
$={180}^{\circ }-({35}^{\circ }+{60}^{\circ })={180}^{\circ }-{95}^{\circ }={85}^{\circ }$
$x=\angle DBC={85}^{\circ }.(DB\parallel CE,alt.\angle sareequal)$