If m∠BOA is 180° and m∠BOC is 110° , what is the measure of ∠COA?

Answer 1

To find the measure of angle \( \angle COA \), we can use the fact that the sum of the angles around point \( O \) is \( 360^\circ \).

Given:

• \( m\angle BOA = 180^\circ \)
• \( m\angle BOC = 110^\circ \)

We can express the relationship as: \[ m\angle BOA + m\angle BOC + m\angle COA = 360^\circ \] Substituting the known values: \[ 180^\circ + 110^\circ + m\angle COA = 360^\circ \] Now, combine \( 180^\circ \) and \( 110^\circ \): \[ 290^\circ + m\angle COA = 360^\circ \] To find \( m\angle COA \), subtract \( 290^\circ \) from both sides: \[ m\angle COA = 360^\circ - 290^\circ = 70^\circ \]

Therefore, the measure of \( \angle COA \) is \( 70^\circ \).