Answer:
Option C.
Step-by-step explanation:
Given information: Line PA and PB tangent to the circle, [tex]\angle P=36^{\circ}[/tex].
Draw the radius from the point A and B.
The tangent to a circle is perpendicular to the radius at the point of tangency.
[tex]\angle PAO=\angle PBO=90^{\circ}[/tex]
OAPB is a quadrilateral and the sum of all interior angles of a quadrilateral is 360°.
[tex]\angle AOB+\angle PAO+\angel APB+\angle PBO=360[/tex]
[tex]\angle AOB+90+36+90=360[/tex]
[tex]\angle AOB+216=360[/tex]
Subtract 216 from both sides.
[tex]\angle AOB=360-216[/tex]
[tex]\angle AOB=144[/tex]
The measure of arc AB is 144°.
Therefore, the correct option is C.
