Answer:
[tex]64^\circ[/tex]
Step-by-step explanation:
Please refer to the attached figure for the labeling and construction in the given figure:
Given that minor angle of arc AB is [tex]116^\circ[/tex].
Or in other words, we can say that angle subtended on the center O by the arc is [tex]116^\circ[/tex].
Now, PA and PB are the tangents so, if we join the center of circle O with A and B, the angles formed are right angles.
i.e.
[tex]\angle PAO = 90^\circ\\\angle PBO = 90^\circ[/tex]
Now, we know that sum of internal angles of a quadrilateral is equal to [tex]360^\circ[/tex].
Here, we have the quadrilateral AOPB.
[tex]\therefore \angle PAO +\angle PBO+\angle AOB +\angle APB=360^\circ\\\Rightarrow 90+90+116+x=360^\circ\\\Rightarrow x = 360 - 180 - 116\\\Rightarrow x = 64^\circ[/tex]
Hence, the correct answer is:
[tex]x = 64^\circ[/tex]
