Finding Angle at $\gamma$ - Help Requested

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In summary, the person is asking for the theorem to use in order to find the angle at $\gamma$. They have already worked out the rest but are unsure about this particular angle. The suggested theorem is the vertical angles theorem, but the person clarifies that this only gives the angle between two straight lines. They mention that $\gamma$ may be the angle between those two lines, which would make things easier. Ultimately, they thank the person for their help.
  • #1
Carla1985
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Hi,

could someone please tell me what theorem I need to be looking at to work out the angle at $\gamma$ please? I've worked out the rest but can't find a theorem for this one.

Thanks
 

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  • #2
Use the vertical angles theorem.
 
  • #3
Euge said:
Use the vertical angles theorem.

Thanks but that just gives me the angle between the two straight lines. My impression was that $\gamma$ was the part of the angle up to the edge of the circle.
 
  • #4
That would not make an angle, for an angle is formed by two straight lines. It would only make sense for $gamma$ to be the angle between those two lines.
 
  • #5
Euge said:
That would not make an angle, for an angle is formed by two straight lines. It would only make sense for $gamma$ to be the angle between those two lines.

That would make things a whole lot easier. Thank you for your help!
 

FAQ: Finding Angle at $\gamma$ - Help Requested

What is the "Finding Angle at $\gamma$" problem?

The "Finding Angle at $\gamma$" problem is a mathematical problem where the goal is to find the measure of angle $\gamma$ in a triangle, given the measures of the other two angles.

Why is it important to be able to find the angle at $\gamma$?

Being able to find the angle at $\gamma$ is important in many practical applications, such as construction, engineering, and navigation. It is also an important concept in geometry and trigonometry, and is used in various mathematical proofs and calculations.

What are the steps for solving the "Finding Angle at $\gamma$" problem?

The steps for solving the "Finding Angle at $\gamma$" problem are:

  • 1. Identify the given values: the measures of the other two angles in the triangle.
  • 2. Use the fact that the sum of the angles in a triangle is 180 degrees to find the measure of angle $\gamma$.
  • 3. If necessary, use other known properties of triangles, such as the Pythagorean theorem or the law of sines or cosines, to find the measure of angle $\gamma$.

Can the "Finding Angle at $\gamma$" problem be solved without using trigonometry?

Yes, the "Finding Angle at $\gamma$" problem can be solved without using trigonometry. If the triangle is a right triangle, the Pythagorean theorem can be used to find the measure of angle $\gamma$. If the triangle is not a right triangle, other properties of triangles, such as the angle sum property, can be used to find the measure of angle $\gamma$.

Are there any shortcuts or tricks for solving the "Finding Angle at $\gamma$" problem?

There are no general shortcuts or tricks for solving the "Finding Angle at $\gamma$" problem. However, there may be specific strategies or techniques that can be used for certain types of triangles or special cases. It is important to have a good understanding of basic geometry and trigonometry concepts in order to be able to effectively solve this problem.

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