To find the measure of angle \( \angle COA \), you can use the fact that the sum of angles around point \( O \) must equal \( 360^\circ \).
Given:
- \( m\angle BOA = 180^\circ \)
- \( m\angle BOC = 110^\circ \)
To find \( m\angle COA \), you can use the equation:
\[ m\angle COA = 360^\circ - (m\angle BOA + m\angle BOC) \]
Now substitute the values:
\[ m\angle COA = 360^\circ - (180^\circ + 110^\circ) \]
\[ m\angle COA = 360^\circ - 290^\circ \]
\[ m\angle COA = 70^\circ \]
Thus, the measure of \( \angle COA \) is \( 70^\circ \).