Answer:
The correct option is B.
Step-by-step explanation:
From the given graph it is clear that the measure of arc AB is 100°.
Let the center of circle of the circle be O.
According to the central angle theorem, the angled inscribed on a circle is half of its central angle.
Using central angle theorem,
[tex]\angle ABX=\frac{1}{2}\times \angle AOX[/tex]
[tex]42^{\circ}=\frac{1}{2}\times \angle AOX[/tex]
Multiply 2 on both the sides.
[tex]42^{\circ}\times 2=\angle AOX[/tex]
[tex]84^{\circ}=\angle AOX[/tex]
The central angle of arc AX is 84°. So the measure of arc AX is 84°.
Using tangent secant theorem,
[tex]\text{Angle between tangent and secant}=\frac{1}{2}(\text{Major arc - Minor arc})[/tex]
[tex]\angle ACB=\frac{1}{2}(Arc(AB)-Arc(AX))[/tex]
[tex]\angle ACB=\frac{1}{2}(100^{\circ}-84^{\circ})[/tex]
[tex]\angle ACB=\frac{1}{2}(16^{\circ})[/tex]
[tex]\angle ACB=8^{\circ}[/tex]
Therefore the measure of angle ACB is 8° Therefore the correct option is B.
