A) \[{{30}^{o}},\,\,{{45}^{o}},\,\,86\]
B) \[{{48}^{o}},\,\,{{36}^{o}},\,\,96\]
C) \[{{48}^{o}},\,\,{{36}^{o}},\,\,{{90}^{o}}\]
D) \[{{36}^{o}},\,\,{{45}^{o}},\,\,{{96}^{o}}\]
Correct Answer: B
Solution :
Given, \[x=\frac{4}{3}y,y=\frac{3}{8}z\]or \[z=\frac{8}{3}y\] \[AB||CD\]and BC is transversal \[\therefore \]\[\angle ABC+\angle DCB={{180}^{o}}\](co-interior angles) \[\therefore \]\[x+y+z={{180}^{o}}\] \[\Rightarrow \] \[\frac{4}{3}y+y\frac{8}{3}y={{180}^{o}}\] \[\therefore \]\[15y={{180}^{o}}\times 3\Rightarrow y={{36}^{o}}\] \[\therefore \]\[x=\frac{4}{3}({{36}^{o}})={{48}^{o}}\]and \[z=\frac{8}{3}({{36}^{o}})={{96}^{o}}\]
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