How Do I Calculate Angle BAC if Angle CBA is 69 Degrees?

  • Thread starter Natasha1
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You are correct.In summary, the conversation discusses a quadrilateral inscribed in a circle and the measures of its angles. The group discusses the inscribed angle theorem and possible solutions for finding angle BAC. There is confusion about the measurements and markings on the diagram, but they eventually determine that the measure of angle BAC is 48 degrees.
  • #1
Natasha1
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Homework Statement
The diagram shows a circle with centre O.
Relevant Equations
A, B, C and D lie on the circumference of the circle. Work out angle BAC
Please see attached drawing which I have written my work (in colour).

Despite spending 1h on it I still can’t understand how to find angle BAC.

776B6095-1913-4498-8E36-8FE05139D586.jpeg
 
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  • #2
I found it! It’s 48 degrees
 
  • #3
1) For a quadrilateral inscribed in a circle, the sum of opposite angles equals to 180 degrees.
2) Inscribed angle theorem
 
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  • #4
Natasha1 said:
I found it! It’s 48 degrees
In that case BD would be parallel to BA which it is plainly not. There is a 48 degree angle where you've marked 58. I'm not sure we can solve for BAC since chord DA's length can be shrunk or stretched without materially affecting the rest of the given geometry. Sum of angles BAC and ABD should be 48 by exterior angle thm.
 
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  • #5
neilparker62 said:
I'm not sure we can solve for BAC since chord DA's length can be shrunk or stretched without materially affecting the rest of the given geometry.
Not by moving A because that would change ABC, and if you move D then BAC doesn't change anyway.
neilparker62 said:
In that case BD would be parallel to BA

How do you deduce that? I agree with 48 degrees.
 
  • #6
Maybe I am misinterpreting the marked angles ? Why has the OP marked 58 degrees when the other 2 angles in the triangle are 63 and 69 degrees. I think the confusion arises because I thought (and it looks like the OP also initially thought) that the measure of angle CBD was 69 degrees. But now I see it's CBA which is 69 degrees. Then the 48 degree answer makes sense.

If a person thought CBD was 69 degrees, he/she would also mark CAD as 69 degrees as appears to be the case.
 
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  • #7
neilparker62 said:
it's CBA which is 69 degrees
Yes.
 

Related to How Do I Calculate Angle BAC if Angle CBA is 69 Degrees?

1. What is Angle BAC?

Angle BAC is a geometric term that refers to the angle formed by the two rays BA and BC at point A. It is commonly used in geometry and trigonometry to measure the angle between two intersecting lines.

2. How do you find Angle BAC?

To find Angle BAC, you will need to know the measurements of the two intersecting lines BA and BC. Then, you can use a protractor to measure the angle or use trigonometric functions such as sine, cosine, or tangent to calculate the angle.

3. Why is Angle BAC important?

Angle BAC is important because it helps us understand the relationship between two intersecting lines and the angles they form. It is also used in various real-life applications, such as navigation, engineering, and architecture.

4. What are some properties of Angle BAC?

Some properties of Angle BAC include its measurement in degrees or radians, its position in relation to other angles, and its ability to be bisected into two equal angles. Angle BAC is also part of a larger geometric shape, such as a triangle or quadrilateral.

5. Can you help me find Angle BAC if I only know the measurements of the two intersecting lines?

Yes, I can help you find Angle BAC by using trigonometric functions such as sine, cosine, or tangent. These functions can help us calculate the angle based on the known measurements of the intersecting lines. Alternatively, we can also use a protractor to measure the angle directly.

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