Question

What is the measure of angle ACB?

Answer 1

<ACB = 1/2(100 - 42)
<ACB = 1/2(58)
<ACB = 29

answer is A. 29

Answer 2

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,

$\angle ABX=\frac{1}{2}\times \angle AOX$

$42^{\circ}=\frac{1}{2}\times \angle AOX$

Multiply 2 on both the sides.

$42^{\circ}\times 2=\angle AOX$

$84^{\circ}=\angle AOX$

The central angle of arc AX is 84°. So the measure of arc AX is 84°.

Using tangent secant theorem,

$\text{Angle between tangent and secant}=\frac{1}{2}(\text{Major arc - Minor arc})$

$\angle ACB=\frac{1}{2}(Arc(AB)-Arc(AX))$

$\angle ACB=\frac{1}{2}(100^{\circ}-84^{\circ})$

$\angle ACB=\frac{1}{2}(16^{\circ})$

$\angle ACB=8^{\circ}$

Therefore the measure of angle ACB is 8° Therefore the correct option is B.