Question

Find the numerical value for x. 40° to 40°

Answer 1

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:

`\begin{gathered} 2m\angle y=\hat{AB} \\ 2\cdot50=\hat{AB} \\ 100=\hat{AB} \end{gathered}`

Therefore, the measure of arc BC is 180° - 100° = 80°

angle x is related to arc AD and arc CB as follows:

`\begin{gathered} m\angle x=(1)/(2)(\hat{AD}+\hat{BC}) \\ m\angle x=(1)/(2)(40+80) \\ m\angle x=60\text{ \degree} \end{gathered}`