Answer:
Option A. The measure of angle C is 140°
Explanation:
see the attached figure with letters to better understand the problem
we know that
The triangle OAB is an isosceles triangle
Because
OA=OB=radius
m∠BAO=m∠ABO=20°
Find the measure of angle C
Remember that the sum of the interior angles of a triangle must be equal to 180 degrees
so
m∠BAO+m∠ABO+m∠C=180°
substitute the given values
20°+20°+m∠C=180°
m∠C=180°-40°=140°