A) \[{{40}^{o}}\]
B) \[{{20}^{o}}\]
C) \[{{100}^{o}}\]
D) \[{{30}^{o}}\]
Correct Answer: B
Solution :
In the given figure, \[AB||CD\] \[\Rightarrow \]\[\angle PEB=\angle PGD={{80}^{o}}\](corresponding angles) Now, EGQ is a straight line. \[\therefore \]\[\angle EGD+\angle DGQ={{180}^{o}}\](linear pair) \[\Rightarrow \] \[\angle DGQ={{100}^{o}}\] Now, \[\angle QHD=x+\angle DGQ\](exterior angle property) \[\Rightarrow \]\[{{120}^{o}}=x+{{100}^{o}}\Rightarrow x={{20}^{o}}\]
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