Question

question 4 of 10
what is the measure of \\( \overparen { a c } \\) ?
a. \\( 30 ^ { \circ } \\)
b. \\( 120 ^ { \circ } \\)
c. \\( 150 ^ { \circ } \\)
d. \\( 90 ^ { \circ } \\)

Explanation:

Step1: Find the measure of the central angle for arc \(AC\)

The sum of angles around point \(B\) is \(360^{\circ}\). We know one angle is \(90^{\circ}\), and another is \(30^{\circ}+ 90^{\circ}=120^{\circ}\) (the angle adjacent to the \(30^{\circ}\) and the right - angle at \(B\) for the line \(AE\) and the radius \(BC\)).
The measure of the central angle for arc \(AC\): \(360^{\circ}-(90^{\circ}+120^{\circ}) = 150^{\circ}\)

Answer:

C. \(150^{\circ}\)