Question

r
m
m∠boc=
m∠aob=

Explanation:

Step1: Find \(m\angle AOB\)

Vertical angles are equal. \(\angle AOB\) and the \(54^{\circ}\) angle are vertical angles.
\(m\angle AOB = 54^{\circ}\)

Step2: Find \(m\angle BOC\)

\(\angle AOB\), \(\angle BOC\) and \(27^{\circ}\) form a straight line (\(180^{\circ}\)).
\(m\angle BOC=180^{\circ}-27^{\circ}-m\angle AOB\)
Substitute \(m\angle AOB = 54^{\circ}\) into the formula:
\(m\angle BOC=180^{\circ}-27^{\circ}-54^{\circ}=99^{\circ}\)

Answer:

\(m\angle AOB = 54^{\circ}\), \(m\angle BOC = 99^{\circ}\)