A) \[22.5{}^\circ \]
B) \[25{}^\circ \]
C) \[30{}^\circ \]
D) \[45{}^\circ \]
Correct Answer: A
Solution :
Let \[\angle XOB=\theta \] In \[\Delta OXB,\] \[\angle XOB+\angle OBX+\angle OXB=180{}^\circ \] \[\Rightarrow \]\[\theta +45{}^\circ +\angle OXB=180{}^\circ \] \[\Rightarrow \]\[\angle OXB=180{}^\circ -45{}^\circ -\theta =135{}^\circ -\theta \] Here, \[\angle OXA+\angle OXB=180{}^\circ \] \[\Rightarrow \]\[\angle OXA+135{}^\circ -\theta =180{}^\circ \] \[\Rightarrow \]\[\angle OXA=45{}^\circ +\theta \] In \[\Delta OXA,\]\[AO=OX\] \[\therefore \]\[\angle OXA=\angle AOX=45{}^\circ +\theta \] (Given) Since, \[\angle AOX+\angle XOB=90{}^\circ \] \[\Rightarrow \]\[45{}^\circ +\theta +\theta =90{}^\circ \Rightarrow 2\theta =45{}^\circ \Rightarrow \theta =225{}^\circ \]You need to login to perform this action.
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