The points A, B, C, D, E, F, G, and H all lie on the circumference of the circle. We will use properties of cyclic quadrilaterals and angles subtended by the same arc.

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The points A, B, C, D, E, F, G, and H all lie on the circumference of the circle. We will use properties of cyclic quadrilaterals and angles subtended by the same arc.

1. Determine $w$

• Consider the cyclic quadrilateral ABEH.
• The sum of opposite angles in a cyclic quadrilateral is $180^\circ$.
• Therefore, $\angle ABE + \angle AHE = 180^\circ$.
• We are given $\angle ABE = 120^\circ$.
• So, $120^\circ + w = 180^\circ$.