In the figure given above, YAX is a tangent to the circle with centre O, If \[\angle BAX=70{}^\circ \] and \[\angle BAQ=40{}^\circ ,\]then what is \[\angle ABQ\] is equal to?
A) \[20{}^\circ \]
B) \[30{}^\circ \]
C) \[35{}^\circ \]
D) \[40{}^\circ \]
Correct Answer: B
Solution :
| Given, \[\angle BAX=70{}^\circ \] and \[\angle BAQ=40{}^\circ \] |
| \[\angle QAX=70{}^\circ -40{}^\circ =30{}^\circ \] |
| \[\therefore \] \[\angle EAX=90{}^\circ \] |
| \[\Rightarrow \] \[\angle EAB=90{}^\circ -70{}^\circ =20{}^\circ \] |
 |
| Since, \[AQBE\]is a cyclic quadrilateral. |
| \[\therefore \] \[\angle EAQ+\angle EBQ=180{}^\circ \] |
| \[\Rightarrow \] \[\angle EBQ=180{}^\circ -60{}^\circ =120{}^\circ \] |
| But \[\angle EBA=90{}^\circ \] |
| \[\therefore \] \[\angle ABQ=120{}^\circ -90{}^\circ =30{}^\circ \] |
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