In circle A shown below, Line BD is a diameter and the measure of Arc CB is 54°:
What is the measure of ∠ DBC?

- becca9898

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- becca9898

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- mathstudent55

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- becca9898

54°
36°
27°
63°
I think the answer is 27, but I am unsure

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## More answers

- mathstudent55

Are you sure the question is angle DBC? There is no angle DBC shown in your figure.

- becca9898

I am sure of it. Let me take a screenshot of the question

- mathstudent55

We can find the answer. I just want to make sure we have the correct question.

- mathstudent55

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- becca9898

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- becca9898

If this helps, here is the question :)

- mathstudent55

Ok. Notice my first drawing above.
The measure of an inscribed angle is half the arc.

- mathstudent55

They do tell you that BD is a diameter.
Think of angle BAD. It is a straight angle. What is the measure of a straight angle?

- becca9898

Would I use the Inscribed Angle Theorem?
I used DBC = 1/2 * 57

- mathstudent55

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- mathstudent55

I think you meant 54 not 57, but that is still incorrect.
What you did would be correct for angle BDC.
You are being asked about angle DBC, though.

- becca9898

Oops, yes I meant 54.

- mathstudent55

You need to find the arc that angle DBC intercepts.

- mathstudent55

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- mathstudent55

Angle DBC intercepts arc CD.
Do you see that?

- becca9898

I see that.

- mathstudent55

Now we need to find the measure of arc CD.
Then angle DBC is half the measure of arc CD.

- anonymous

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- mathstudent55

A diameter is made up of two radii.
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- mathstudent55

What is the measure of the angle formed by two radii that are a diameter?
Hint: think of a straight angle.

- becca9898

180 degrees?

- mathstudent55

Yes.
A central angle intercepts an arc of the same measure.

- mathstudent55

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- mathstudent55

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- mathstudent55

Arc BCD is intercepted by diameter BD.
Diameter BD is a straight angle of 180 degrees, so arc BCD measures 180 degrees.

- mathstudent55

Arc BC measures 54 deg.
Arc BCD measures 180 deg.
What is the measure of arc CD?

- becca9898

126?

- mathstudent55

Great.
Now let's go back to this figure.
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- mathstudent55

The angle you want is the inscribed angle that intercepts arc CD, so its measure is half of arc CD.

- becca9898

So that would be 63? :)

- mathstudent55

Exactly.

- becca9898

Awesome!!! Thank you so much. It makes a lot more sense now!

- mathstudent55

You're welcome.

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