In the figure, PA is a tangent from an external point P to the circle with centre O. If $\angle POB = 110^\circ$, then the measure of $\angle APO$ is:
Answer & explanation
Correct answer: option 4
\(\angle\)POB = \({110}^\circ\)
\(\angle\)POB + \(\angle\)POA = 180
= 110 + \(\angle\)POA = 180
= \(\angle\)POA = 180 - 110 = 70
\(\angle\)OAP = 90
In triangle APO
\(\angle\)APO + \(\angle\)POA + \(\angle\)OAP = 180
= \(\angle\)APO + 70 + 90 = 180
= \(\angle\)APO = 180 - 90 - 70 = \({20}^\circ\).