question_answer

In the following figure, if\[\angle PQA=20{}^\circ ,\]then find the value of \[\angle PAQ.\]

A)  \[120{}^\circ \]

B)  \[40{}^\circ \]

C)  \[20{}^\circ \]             

D)  \[70{}^\circ \]

Correct Answer: D

Solution :

Diameter = OP and AP line touches the circle. \[\therefore \] \[\angle OPA\,=90{}^\circ \] \[\therefore \] \[x=180{}^\circ -(90{}^\circ +20{}^\circ )=180{}^\circ -110{}^\circ =70{}^\circ \]