the segment AC is the diameter of the circle
Then, the arc AC measures 180°
angle y measures 180° - 90° - 40° = 50°
angle y is related to arc AB as follows:
[tex]\begin{gathered} 2m\angle y=\hat{AB} \\ 2\cdot50=\hat{AB} \\ 100=\hat{AB} \end{gathered}[/tex]Therefore, the measure of arc BC is 180° - 100° = 80°
angle x is related to arc AD and arc CB as follows:
[tex]\begin{gathered} m\angle x=\frac{1}{2}(\hat{AD}+\hat{BC}) \\ m\angle x=\frac{1}{2}(40+80) \\ m\angle x=60\text{ \degree} \end{gathered}[/tex]
