Question

What is the measure of AC?

Answer 1

Answer: B. $150^{\circ}$

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 : $90^{\circ}$

The measure of minor arc : $30^{\circ}$

The formula to find the internal angle is given by :-

$\theta=\dfrac{\text{Minor arc + major arc}}{2}$

Let x be the Major arc AC, the we have the following equation:-

$90^{\circ}=\dfrac{30^{\circ}\text{ + x}}{2}\\\\\Rightarrow\ 30^{\circ}+x=180^{\circ}\\\\\Rightarrow\ x=180^{\circ}-30^{\circ}\\\\\Rightarrow\ x=150^{\circ}$

Hence, the measure of $\overarc{AC}=150^{\circ}$

Answer 2

The answer is:
D.90
I hope I helped