A) \[{{75}^{o}}\] and \[{{20}^{o}}\]
B) \[{{20}^{o}}\] and \[{{75}^{o}}\]
C) \[{{25}^{o}}\] and \[{{70}^{o}}\]
D) \[{{70}^{o}}\] and \[{{25}^{o}}\]
Correct Answer: D
Solution :
The lines AB and EF intersect at G. \[\therefore \] \[\angle EGB=\angle AGF\] (Vertically opposite angles) \[\Rightarrow \] \[\angle AGF={{65}^{o}}\] Since \[AB||CD,\] \[\angle GHD=\angle AGH=\angle AGF\] \[\Rightarrow \] \[\angle GHD={{65}^{o}}\] \[\Rightarrow \] \[\angle GHO+\angle OHD={{65}^{o}}\] \[\Rightarrow \] \[{{q}^{o}}={{65}^{o}}-{{40}^{o}}={{25}^{o}}\] Draw a line XY through ?O? parallel to AB and CD. Since \[XY||AB,\] \[\angle XOG=\angle BGO\] \[\Rightarrow \] \[\angle XOG={{45}^{o}}\] (Alternate angles) and \[XY||CD\,\,\,\Rightarrow \,\,\,\angle XOH=\angle OHD\] \[\Rightarrow \] But &You need to login to perform this action.
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