Question
Triangle ABC 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
Answers
GPT-4o mini
In a circle, the inscribed angle is half the measure of the arc that subtends it. Since triangle ABC is inscribed in a circle and AB is the diameter, angle ACB (the inscribed angle at C) subtends arc AB.
Given that angle A measures 15°, arc AC subtends angle A. The measure of an inscribed angle (angle A) is half the measure of the arc opposite to that angle (arc AC). Therefore:
\[
\text{measure of arc AC} = 2 \times \text{angle A} = 2 \times 15° = 30°
\]
Thus, the measure of arc AC is \( \boxed{30} \) degrees.
Given that angle A measures 15°, arc AC subtends angle A. The measure of an inscribed angle (angle A) is half the measure of the arc opposite to that angle (arc AC). Therefore:
\[
\text{measure of arc AC} = 2 \times \text{angle A} = 2 \times 15° = 30°
\]
Thus, the measure of arc AC is \( \boxed{30} \) degrees.