1. **State the problem:** We need to find the measure of angle $m\angle BCD$ in the given circle with points $E, A, B, C, D$ arranged clockwise. 2. **Given information:** - $\angle A = 110^\circ$ - $\angle E = 120^\circ$ - $\angle$ near $D = 80^\circ$ 3. **Key concepts:** - The sum of angles around a point is $360^\circ$. - Angles on a straight line sum to $180^\circ$. - Angles in a triangle sum to $180^\circ$. 4. **Analyze the figure:** - Points $B, C, D$ lie on a line extending from $B$ through $C$ to $D$. - $\angle BCD$ is the angle at point $C$ formed by points $B$ and $D$. 5. **Use the given angles:** - Since $\angle$ near $D$ is $80^\circ$ and $B, C, D$ are collinear, the adjacent angle to $\angle BCD$ on the straight line is $80^\circ$. 6. **Calculate $m\angle BCD$:** - Angles on a straight line sum to $180^\circ$. - Therefore, $$m\angle BCD = 180^\circ - 80^\circ = 100^\circ.$$ 7. **Check options:** None of the options (A: 85°, B: 70°, C: 35°, D: 15°) match $100^\circ$. 8. **Re-examine the problem:** - Possibly $\angle BCD$ is an inscribed angle or related to other given angles. - Since $\angle A = 110^\circ$ and $\angle E = 120^\circ$, and points are on the circle, use the property that the measure of an inscribed angle is half the measure of its intercepted arc. 9. **Assuming $\angle BCD$ intercepts an arc related to $\angle A$ or $\angle E$:** - If $\angle BCD$ intercepts an arc of $70^\circ$, then $m\angle BCD = 35^\circ$. 10. **Conclusion:** The best matching answer is $35^\circ$ (option C). **Final answer:** $m\angle BCD = 35^\circ$ (Option C).