A) \[{{100}^{o}}\]
B) \[{{76}^{o}}\]
C) \[{{82}^{o}}\]
D) \[{{122}^{o}}\]
Correct Answer: A
Solution :
Given that \[AB||CD\]and \[CD||EF\] \[\therefore \]\[AB||CD||EF\] \[x+y={{180}^{o}}\] ?(i)(co-interior angles) \[y+z={{180}^{o}}\] ?(ii) \[[\angle DHl=y,\] (vertically opposite angles] Give that \[y:z\Rightarrow 4:5\Rightarrow y=\frac{4}{5}z\] Substituting in (ii), we get \[\frac{4z}{5}+z={{180}^{o}}\Rightarrow \frac{9z}{5}={{180}^{o}}\] \[\Rightarrow \]\[z=\frac{{{180}^{o}}\times 5}{9}\Rightarrow z={{100}^{o}}\] Subsuming value of z in (ii), we get \[y+{{100}^{o}}={{180}^{o}}\Rightarrow y={{80}^{o}}\] From (i), we have \[x+{{80}^{o}}={{180}^{o}}\Rightarrow x={{100}^{o}}\]
You need to login to perform this action.
You will be redirected in
3 sec
