Find \[\angle x\] and \[\angle y\] respectively.
A) \[{{50}^{o}},{{49}^{o}}\]
B) \[{{59}^{o}},{{40}^{o}}\]
C) \[{{59}^{o}},{{59}^{o}}\]
D) \[{{49}^{o}},{{48}^{o}}\]
Correct Answer: C
Solution :
[a] As, \[\angle AJB+\angle BJC+\angle CJD+\angle DJE={{180}^{o}}\] (Angles on a straight line AE) \[\therefore \] \[{{42}^{o}}+\angle x+{{40}^{o}}+{{39}^{o}}={{180}^{o}}\] \[\angle x={{180}^{o}}-({{42}^{o}}+{{40}^{o}}+{{39}^{o}})\] \[\angle x={{180}^{o}}-{{121}^{o}}={{59}^{o}}\] [b] \[\angle y=\angle x\] (Vertically opposite angles) \[\therefore \] \[\angle y={{59}^{o}}\]
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