Find the measure of c in the picture

Option A. The measure of angle C is 140°

Step-by-step 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°

answer is 270 degrees: -

to convert radians to degrees you multiply by 180/π

9π/ 6 * 180 / π

=   9 * 180 / 6

= 9 * 30

=   270 degrees   answer