Answer:
See image
Step-by-step explanation:
For this question, you need to know several special relationships about circles. A radius goes from the center of a circle to any point on the circle. All the radii (not a typo, plural of radius is radii) are the same size, their measures are equal; we say they are congruent (the symbol is an equal sign with a ~over it)
In the diagram, OA and OB are congruent because they are radii. AC is a tangent, that means that it touches the circle at exactly one point, in this case at A. So since OA is a radius and AC is a tangent, they are perpendicular to each other (makes 90° angles). Then we can subtract 90 - 72 to find the angle OAB. Angle OAB is 14°. In triangle AOB, which has two sides the same, the opposite angles will also be congruent which means OBA is also 14° (OR you could use the exact same logic for OB perpendicular to BC and subtract, same calculation as before) . Once you have the two 14° angles in the triangle, you can use the fact that all the angles in a triangle add up to 180° So then, 14 + 14 + x =180. Solve this equation to find angle AOB. See image.
