Question 3: The vertices of the quadrilaterals below lie on the circumference of the circle. Determine the value of the unknown variables.

Question 3: The vertices of the quadrilaterals below lie on the circumference of the circle. Determine the value of the unknown variables.

We need to find the values of $x, y, z,$ and $w$.

Step 1: Find $x$.
The angle $x$ is $\angle BCS$.
Consider the cyclic quadrilateral ABRS.
The sum of opposite angles in a cyclic quadrilateral is $180^\circ$.
We are given $\angle BAS = 60^\circ$.
Therefore, $\angle BRS + \angle BAS = 180^\circ$.

$$\angle BRS + 60^\circ = 180^\circ$$ $$$$