A)
x y z \[{{20}^{o}}\] 80 \[{{140}^{o}}\]
B)
x y z \[{{30}^{o}}\] \[{{80}^{o}}\] \[{{140}^{o}}\]
C)
x y z \[{{20}^{o}}\] \[{{100}^{o}}\] \[{{160}^{o}}\]
D)
x y z \[{{30}^{o}}\] \[{{100}^{o}}\] \[{{160}^{o}}\]
Correct Answer: C
Solution :
As, \[y=5x\] In \[\Delta RQS,\] \[x+y+{{60}^{o}}={{180}^{o}}\](Angle sum property) \[\Rightarrow \] \[x+5x+{{60}^{o}}={{180}^{o}}\] \[\Rightarrow \] \[6x={{180}^{o}}-{{60}^{o}}={{120}^{o}}\Rightarrow x=\frac{{{120}^{o}}}{6}={{20}^{o}}\] \[\therefore \] \[y=5\times {{20}^{o}}={{100}^{o}}\] Also \[\angle QRS+\angle QSR=z\] (Exterior angle property) \[\Rightarrow \] \[z={{60}^{o}}+{{100}^{o}}={{160}^{o}}\]
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