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Question
Math
Posted 2 months ago

Angle CC is inscribed in circle OO.
AB\overline{A B} is a diameter of circle OO.
What is the measure of A\angle A ?
O\mathrm{O}
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Answer from Sia
Posted 2 months ago
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 C\angle C is the arc from point A to point B, which is a semicircle
step 3
Since AB\overline{AB} is a diameter, the arc measures 180180^\circ
step 4
Calculate the measure of A\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 A\angle A is 12×180=90\frac{1}{2} \times 180^\circ = 90^\circ
1 Answer
The measure of A\angle A is 9090^\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.

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