Question

Math

Posted 3 months ago

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

Sign in to unlock the answer

Answer from Sia

Posted 3 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 $\angle C$ 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 $\frac{1}{2} \times 180^\circ = 90^\circ$

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.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Upgrade to Asksia Pro

Join a AskSia's Pro Plan, and get 24/7 AI tutoring for your reviews, assignments, quizzes and exam preps.

Unlimited chat query usages

Strong algorithms that better know you

Early access to new release features

Study Other Question