Triangle ABC

Question

is inscribed within a circle and has diameter line AB
, with the inscribed angle at C
. If the angle measure of A
is 15°, what is the arc measure of AC
?(1 point)
º

Answer 1

In a triangle inscribed in a circle, if one side of the triangle is a diameter of the circle, then the angle opposite to that side (angle C) is a right angle (90°).

In this case, triangle ABC has AB as its diameter and angle A measures 15°. According to the properties of inscribed angles, the measure of the arc opposite an inscribed angle is twice the measure of that angle.

Thus, since the arc AC is opposite angle A:

\[ \text{Arc } AC = 2 \times \text{Angle } A = 2 \times 15° = 30° \]

Therefore, the arc measure of AC is 30°.