Question

If $CE$ is parallel to $DB$ in the given figure, find the value of 'x'

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

Answer 1

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

R.E.F image

In $\Delta ABD$

$\varphi +{110}^{\circ }+{30}^{\circ }={180}^{\circ }$

$\Rightarrow \varphi ={40}^{\circ }$

As $\varphi +{\theta }_1={75}^{\circ }\Rightarrow {\theta }_1=35$

As $DB$ is Parallel to $CE\therefore {\theta }_1={\theta }_2={35}^{\circ }$

$\Rightarrow {\theta }_2+x+{60}^{\circ }={180}^{\circ }\Rightarrow x={85}^{\circ }$