WAEC math obj answer

Step 1: Use the property of angles formed by intersecting chords.
The angle formed by two intersecting chords (MQ and NP) inside a circle is half the sum of the measures of the intercepted arcs.
The angle $\angle NFP = (5x)^\circ$ intercepts arcs NP and MQ.
The inscribed angle $\angle NMP = (100-x)^\circ$ subtends arc NP. Therefore, $\text{arc NP} = 2 \times \angle NMP = 2(100-x)^\circ$.
The inscribed angle $\angle MNQ = y^\circ$ subtends arc MQ. Therefore, $\text{arc MQ} = 2 \times \angle MNQ = 2y^\circ$.
So, we have