If m∠BOA

Question

is 180°
and m∠BOC
is 110°
, what is the measure of ∠COA
?(1 point)
$$
a
Remaining Attempts : 2View previous attempt

Answer 1

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

Given:

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

Since \(m\angle BOA\) and \(m\angle BOC\) share point \(O\) and there are two angles around it, we can define the angles involved:

\[ m\angle AOB + m\angle BOC + m\angle COA = 360^\circ \]

We know:

1. \(m\angle BOA = 180^\circ\)
2. \(m\angle BOC = 110^\circ\)

Now, since \(\angle AOB\) and \(\angle BOC\) are not directly adjacent, we can rewrite:

\[ m\angle COA + 110^\circ = 180^\circ \]

This is because \(m\angle BOA\) (which is \(180^\circ\)) is formed by the sum of \(m\angle BOC\) and \(m\angle COA\):

\[ m\angle COA = 180^\circ - m\angle BOC \]

Substituting \(m\angle BOC\):

\[ m\angle COA = 180^\circ - 110^\circ = 70^\circ \]

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

Thus, the answer is: \[ \boxed{70^\circ} \]