Answer:
[tex]m\angle BOC=54^\circ[/tex]
Step-by-step explanation:
First, we establish the following:
Therefore:
[tex]\angle BAC$ is the angle subtended by arc BC on the circumference.\\\angle BOC$ is the angle subtended by arc BC at the centre.[/tex]
The inscribed angle theorem states that an angle inscribed in a circle is half of the central angle that subtends the same arc on the circle.
Therefore:
[tex]\angle BOC =2\angle BAC\\\angle BOC=2 \times 27\\m\angle BOC=54^\circ[/tex]
