becca9898
  • becca9898
In circle A shown below, Line BD is a diameter and the measure of Arc CB is 54°: What is the measure of ∠ DBC?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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becca9898
  • becca9898
|dw:1439250086914:dw|
mathstudent55
  • mathstudent55
|dw:1439246526551:dw|
becca9898
  • becca9898
54° 36° 27° 63° I think the answer is 27, but I am unsure

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mathstudent55
  • mathstudent55
Are you sure the question is angle DBC? There is no angle DBC shown in your figure.
becca9898
  • becca9898
I am sure of it. Let me take a screenshot of the question
mathstudent55
  • mathstudent55
We can find the answer. I just want to make sure we have the correct question.
mathstudent55
  • mathstudent55
|dw:1439246714171:dw|
becca9898
  • becca9898
1 Attachment
becca9898
  • becca9898
If this helps, here is the question :)
mathstudent55
  • mathstudent55
Ok. Notice my first drawing above. The measure of an inscribed angle is half the arc.
mathstudent55
  • 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
  • becca9898
Would I use the Inscribed Angle Theorem? I used DBC = 1/2 * 57
mathstudent55
  • mathstudent55
|dw:1439246922903:dw|
mathstudent55
  • 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
  • becca9898
Oops, yes I meant 54.
mathstudent55
  • mathstudent55
You need to find the arc that angle DBC intercepts.
mathstudent55
  • mathstudent55
|dw:1439247095578:dw|
mathstudent55
  • mathstudent55
Angle DBC intercepts arc CD. Do you see that?
becca9898
  • becca9898
I see that.
mathstudent55
  • mathstudent55
Now we need to find the measure of arc CD. Then angle DBC is half the measure of arc CD.
anonymous
  • anonymous
|dw:1439257707805:dw|
mathstudent55
  • mathstudent55
A diameter is made up of two radii. |dw:1439247250424:dw|
mathstudent55
  • mathstudent55
What is the measure of the angle formed by two radii that are a diameter? Hint: think of a straight angle.
becca9898
  • becca9898
180 degrees?
mathstudent55
  • mathstudent55
Yes. A central angle intercepts an arc of the same measure.
mathstudent55
  • mathstudent55
|dw:1439247397295:dw|
mathstudent55
  • mathstudent55
|dw:1439247431302:dw|
mathstudent55
  • mathstudent55
Arc BCD is intercepted by diameter BD. Diameter BD is a straight angle of 180 degrees, so arc BCD measures 180 degrees.
mathstudent55
  • mathstudent55
Arc BC measures 54 deg. Arc BCD measures 180 deg. What is the measure of arc CD?
becca9898
  • becca9898
126?
mathstudent55
  • mathstudent55
Great. Now let's go back to this figure. |dw:1439247652129:dw|
mathstudent55
  • mathstudent55
The angle you want is the inscribed angle that intercepts arc CD, so its measure is half of arc CD.
becca9898
  • becca9898
So that would be 63? :)
mathstudent55
  • mathstudent55
Exactly.
becca9898
  • becca9898
Awesome!!! Thank you so much. It makes a lot more sense now!
mathstudent55
  • mathstudent55
You're welcome.

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