Since line DB is perpendicular to line AC, then arc AB = arc BC
Thus, 14x - 3 = 7x + 18
Collecting like terms,
14x - 7x = 18 + 3
7x = 21
Dividing both sides by 7, we have
[tex]\begin{gathered} x=\frac{21}{7} \\ x=3 \end{gathered}[/tex][tex]\begin{gathered} \angle AC=\angle AOB+\angle BOC \\ \angle AC=14x-3+7x+18 \\ \end{gathered}[/tex]
substituting x into the above equation,
[tex]\begin{gathered} \angle AC=14(3)-3+7(3)+18 \\ \angle AC=42-3+21+18 \\ \angle AC=78^0 \end{gathered}[/tex]
Hence, angle the arc AC makes at the centre is 78 degrees.
