Question

In the given figure, the value of 'z' is _______.

• A. ${120}^{\circ }$
• B. ${85}^{\circ }$
• C. ${80}^{\circ }$
• D. ${140}^{\circ }$

Answer 1

The correct option is D ${140}^{\circ }$


In the figure, $\angle$ BCA and $\angle$ ACE are linear pair.
$\angle$ BCA + $\angle$ ACE $={180}^{\circ }$
${120}^{\circ }+x={180}^{\circ }\Rightarrow x={60}^{\circ }$

From $\Delta$ DCE, we have
${60}^{\circ }+{40}^{\circ }+y^{\circ }={180}^{\circ }$
[Angle sum property]
$\Rightarrow y={80}^{\circ }$

From exterior angle property of a triangle, we have
$x+y=z\Rightarrow z={60}^{\circ }+{80}^{\circ }={140}^{\circ }$
Hence, the value of 'z' is ${140}^{\circ }$.