A) \[{{70}^{o}}\]
B) \[{{50}^{o}}\]
C) \[{{65}^{o}}\]
D) \[{{45}^{o}}\]
Correct Answer: C
Solution :
\[x+{{10}^{o}}+x+x+{{20}^{o}}={{180}^{o}}\] \[\Rightarrow \]\[3x+{{30}^{o}}={{180}^{o}}\Rightarrow 3x={{150}^{o}}\] \[\Rightarrow \]\[x={{50}^{o}}\] \[\angle OCD=\angle ODC\] \[[\because \,OD=OC]\] Now, \[\angle C+\angle D+x={{180}^{o}}\] \[\Rightarrow \]\[\angle OCD+\angle OCD+{{50}^{o}}={{180}^{o}}\] \[\Rightarrow \]\[2\angle OCD={{130}^{o}}\Rightarrow \angle OCD=\angle {{65}^{o}}\]
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