Determine angle w. A, B, C, D, E, F, G, and H all lie on the circumference of the circle.

here are the solutions for , Question 1:

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 $w$

• $w$ is $\angle BHE$.
• Consider the cyclic quadrilateral ABEH.
• The sum of opposite angles in a cyclic quadrilateral is $180^\circ$.
• Therefore, $\angle BAE + \angle BHE = 180^\circ$.
• We are given $\angle BAE = 88^\circ$.
• So,