Answer: B. [tex]150^{\circ}[/tex]
Step-by-step explanation:
From the given picture, we can see a circle with two perpendicularly intersecting chords .
The measure internal angle made by intersecting of chords : [tex]90^{\circ}[/tex]
The measure of minor arc : [tex]30^{\circ}[/tex]
The formula to find the internal angle is given by :-
[tex]\theta=\dfrac{\text{Minor arc + major arc}}{2}[/tex]
Let x be the Major arc AC, the we have the following equation:-
[tex]90^{\circ}=\dfrac{30^{\circ}\text{ + x}}{2}\\\\\Rightarrow\ 30^{\circ}+x=180^{\circ}\\\\\Rightarrow\ x=180^{\circ}-30^{\circ}\\\\\Rightarrow\ x=150^{\circ}[/tex]
Hence, the measure of [tex]\overarc{AC}=150^{\circ}[/tex]
