Angle $C$ is inscribed in circle $O$.
$\overline{A B}$ is a diameter of circle $O$.
What is the measure of $\angle A$ ?
$\mathrm{O}$

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∻Solution by Steps∻ ‖ step 1 ⋮ Recognize that in a circle, an inscribed angle is half the measure of its intercepted arc. ‖ ‖ step 2 ⋮ Identify that the intercepted arc for $\angle C$ is the arc from point A to point B, which is a semicircle. ‖ ‖ step 3 ⋮ Since $\overline{AB}$ is a diameter, the arc measures $180^\circ$. ‖ ‖ step 4 ⋮ Calculate the measure of $\angle A$ by using the inscribed angle theorem, which states that the angle is half the measure of the intercepted arc. ‖ ‖ step 5 ⋮ Therefore, the measure of $\angle A$ is $\frac{1}{2} imes 180^\circ = 90^\circ$. ‖ ∻1 Answer∻ ⚹ The measure of $\angle A$ is $90^\circ$. ⚹ ∻Key Concept∻ ⚹Inscribed Angle Theorem⚹ ∻Explanation∻ ⚹The inscribed angle theorem states that an inscribed angle is half the measure of its intercepted arc. Since the intercepted arc is a semicircle (180 degrees), the inscribed angle is 90 degrees.◊What is the relationship between the measure of an angle inscribed in a circle and the measure of its intercepted arc?⍭ Generate me a similar question◊⚹

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