C

Step 1: From the figure, ∠AOB, ∠COE are vertical angles and m∠AOB = 80 [Vertical angles are congruent.]

Step 2: m∠AOB = m∠COE

Step 3: m∠COE = 80[m∠AOB = 80.]

Step 4: The line OD cuts the angle COE into two equal angles.

Step 5: m∠COE = m∠x + m∠x[Angle addition postulate.]

Step 6: 80 = 2(m∠x)[Substitute the value of ∠COE.]

Step 7: 802 = 2m∠x2[Divide each side by 2.]

Step 8: 40 = m∠x[Simplify.]

Step 9: The measure of x = 40.