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

The correct option is B.

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=(1)/(2)* \angle AOX`

`42^(\circ)=(1)/(2)* \angle AOX`

Multiply 2 on both the sides.

`42^(\circ)* 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}=(1)/(2)(\text{Major arc - Minor arc})`

`\angle ACB=(1)/(2)(Arc(AB)-Arc(AX))`

`\angle ACB=(1)/(2)(100^(\circ)-84^(\circ))`

`\angle ACB=(1)/(2)(16^(\circ))`

`\angle ACB=8^(\circ)`

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