Question

In the figure given, what is $\angle CBA$?

• A. ${30}^o$
• B. ${45}^o$
• C. ${50}^o$
• D. ${60}^o$

Answer 1

The correct option is D ${60}^o$

R.E.F image

$\bullet$ $\angle x+{75}^{\circ }={180}^{\circ }\Rightarrow x={105}^{\circ }$

$\bullet$ In $\Delta CQR\angle x+\angle y+{30}^{\circ }={180}^{\circ }\Rightarrow y={45}^{\circ }$

$\bullet$ $\angle y+\angle z={180}^{\circ }\Rightarrow z={105}^{\circ }$

$\bullet$ In circle quadrilateral $\angle z+\angle \varphi ={180}^{\circ }\Rightarrow \varphi ={45}^{\circ }$

$\bullet$ In $\Delta ABC\angle \theta +\angle \varphi +{75}^{\circ }={180}^{\circ }\Rightarrow \angle \theta ={60}^{\circ }$