A) \[{{92}^{o}}\]
B) \[{{115}^{o}}\]
C) \[{{112.5}^{o}}\]
D) \[{{135.5}^{o}}\]
Correct Answer: C
Solution :
We have, \[c={{75}^{o}}\] \[\therefore \] \[a=\frac{2}{5}c=\frac{2}{5}\times {{75}^{o}}={{30}^{o}}\] Now, \[UT||PQ\] \[\Rightarrow \]\[c=a+b\] (Alternate angles) \[\Rightarrow \] \[{{75}^{o}}={{30}^{o}}+b\,\,\Rightarrow \,\,b={{75}^{o}}-{{30}^{o}}={{45}^{o}}\] Also, \[PQ||RS\] \[\therefore \] \[b+d={{180}^{o}}\] (Co-interior angles) \[\Rightarrow \] \[d={{180}^{o}}-{{45}^{o}}={{135}^{o}}\] So, \[b+\frac{d}{2}={{45}^{o}}+\frac{{{135}^{o}}}{2}={{45}^{o}}+{{67.5}^{o}}={{112.5}^{o}}\]
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