A) \[{{72}^{o}}\]
B) \[{{82}^{o}}\]
C) \[{{90}^{o}}\]
D) \[{{40}^{o}}\]
Correct Answer: A
Solution :
\[\angle UXV=y\] (Vertically opposite angles) \[\therefore \] \[y={{45}^{o}}\] In \[\Delta XYZ\] \[y+x+{{63}^{o}}={{180}^{o}}\] (Angle sum property) \[\Rightarrow \]\[{{45}^{o}}+x+{{63}^{o}}={{180}^{o}}\Rightarrow x={{180}^{o}}-({{45}^{o}}+{{63}^{o}})\] \[\Rightarrow \] \[x={{180}^{o}}-{{108}^{o}}={{72}^{o}}\]
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