Angles?

[BlueFalcon]

I've always wondered this: Is an angle just an arc? For example, when two rays share a common point, that common point is the vertex of the angle, but isn't it also the central point of many arcs? Aren't angles just arcs?

 

[tkhunny]

Good question. Glad to know you're thinking about it.

Arcs are often referred to by their angle measure, but only as they belong to a given distance from the common point (usually the center of a circle)..

An arc requires a definition of a radius, so you can tell which one you're talking about from the "many arcs" you are talking about.

An angle doesn't care how far out you go.

 

[BlueFalcon]

Arcs are often referred to by their angle measure, but only as they belong to a given distance from the common point (usually the center of a circle)..

Could you give me any examples when they are called by their angle measure?

Also, for an angle, I thought normally an angle is really close to the vertex, and not created far from it.

So basically the difference is that an arc has a radius while an angle doesn't?

 

[Steven G]

The angle is NOT necessarily near the vertex.

Do you remember using a compass to measure an angle?? Some compasses are bigger than others! Did the people with the larger compasses get different results compared to the people using the small compasses for the same angle???

 

[Steven G]

An angle can give an arc for any given radius.

Here is one way to draw an arc--with a protractor.

Draw an angles with long sides. Open your protractor to a small opening. Put the needle of the protractor at the vertex and draw an arc from from one leg to the other leg. That is one arc.

Now open your protractor a little wider. Put the needle of the protractor at the vertex and draw an arc from from one leg to the other leg. That is another arc.

You can draw as many arcs as you like for that angle. Is this clear??? And the angle never changed

Alternative you can draw many circles, using your protractor, from the same center point.

Now draw any angle you like using the center point as your vertex. Do you see that each circle you drew gives an arc? Please let me know.

 

[BlueFalcon]

An angle can give an arc for any given radius.

Here is one way to draw an arc--with a protractor.

Draw an angles with long sides. Open your protractor to a small opening. Put the needle of the protractor at the vertex and draw an arc from from one leg to the other leg. That is one arc.

Now open your protractor a little wider. Put the needle of the protractor at the vertex and draw an arc from from one leg to the other leg. That is another arc.

You can draw as many arcs as you like for that angle. Is this clear??? And the angle never changed

Alternative you can draw many circles, using your protractor, from the same center point.

Now draw any angle you like using the center point as your vertex. Do you see that each circle you drew gives an arc? Please let me know.

yes, I do, and I also see how I can make many different sized angles with equal measure. However, from my textbook, it says that an inscribed angle is an angle where its rays contain chords of the circle, and the angle is within the circle. However, the angle is not only within the circle though, by what you're saying, it is also outside the circle right? So is this definition incorrect? Also, with polygons such as triangles, does that mean the interior angles can be formed outside the triangle? Are you saying that arcs are created by angles?

 

[Steven G]

yes, I do, and I also see how I can make many different sized angles with equal measure. No no, the angles are the SAME size. The legs may be longer but the angle is the same.

However, the angle is not only within the circle though, by what you're saying, it is also outside the circle right? Are you saying that because the legs of the angle may go outside a circle with the center being the vertex of the angle then the angle is outside the circle. No, this is not true. An arc may be out of of a circle but the angle is inside the circle by the vertex.

Are you saying that arcs are created by angles? I am not saying that all arcs are created by angles. Surely if you have a circle and you draw two radii you have an arc. So yes, arcs can be created by angles, but I am not sure why you would want to think about that. I can have a circle and highlight part of it and know I have an arc.

 

[BlueFalcon]

No no, the angles are the SAME size.

Oh, so by size it means the measure.

However, the angle is not only within the circle though, by what you're saying, it is also outside the circle right? Are you saying that because the legs of the angle may go outside a circle with the center being the vertex of the angle then the angle is outside the circle. No, this is not true. An arc may be out of of a circle but the angle is inside the circle by the vertex.

So the angle created by two rays/two segments/two lines intersecting is always near the vertex, and anything way further is considered an arc?

 

[Steven G]

Oh, so by size it means the measure.



So the angle created by two rays/two segments/two lines intersecting is always near the vertex, and anything way further is considered an arc?

It is common practice to put the angle symbol near the vertex. That symbol can be an arc if drawn carefully (with a protractor).

Back to a compass: You measure angles with a compass. The compass is quite large compared to the little angle symbol you put near the vertex, yet the compass measure the angles.

What exactly is bothering you about all this? I usually like when a student examine things closely but I do not think (but can be wrong) this is something that should be spending so much time on. You know what an angle is and you know what an arc is. Isn't that enough? Please respond!

 

[JulianMathHelp]

It is common practice to put the angle symbol near the vertex. That symbol can be an arc if drawn carefully (with a protractor).

Back to a compass: You measure angles with a compass. The compass is quite large compared to the little angle symbol you put near the vertex, yet the compass measure the angles.

What exactly is bothering you about all this? I usually like when a student examine things closely but I do not think (but can be wrong) this is something that should be spending so much time on. You know what an angle is and you know what an arc is. Isn't that enough? Please respond!

I am just wondering if angles can be drawn really far away from the vertex.

 

[lev888]

I am just wondering if angles can be drawn really far away from the vertex.

The angle symbols can be drawn anywhere if you want just to draw. If you want to convey information in a clear way, it would make sense to draw them so that it's easy to see, which angles they correspond to.

 

[JulianMathHelp]

The angle symbols can be drawn anywhere if you want just to draw. If you want to convey information in a clear way, it would make sense to draw them so that it's easy to see, which angles they correspond to.

Oh, I’m not talking about angle symbols, I’m talking about angles, and if you are allowed to draw them far away from the vertex.

 

[lev888]

Oh, I’m not talking about angle symbols, I’m talking about angles, and if you are allowed to draw them far away from the vertex.

There is some misunderstanding here. If you have a vertex, you have an angle. It's already there. If we are talking about a triangle, for example, it has 3 vertices and 3 angles. Please clarify what you want to draw.

 

[Steven G]

For any given angles, you can draw the rays from the vertex as long or as short as you like.

 

[JulianMathHelp]

There is some misunderstanding here. If you have a vertex, you have an angle. It's already there. If we are talking about a triangle, for example, it has 3 vertices and 3 angles. Please clarify what you want to draw.

I’m asking if the angle can be drawn far away from the vertex, and not close to it.

 

[Steven G]

Please define what you are calling an angle which you want to know if you can draw far away from the vertex.

The angles is what is formed by the two rays leading away from the vertex.

Again, if you just mean the angles symbol, which is not the angle (it is a symbol!), then it is best to put it near the vertex so others would now that symbol represents the correct angle.

 

[JulianMathHelp]

Is the angle symbol the thing drawn to represent the measure? Is the actual angle not drawable?

 

[Steven G]

Is the angle symbol the thing drawn to represent the measure? Is the actual angle not drawable?

You have a vertex A. Draw 2 rays from A. You now have an angle. You want to call the angle a. So near the vertex you write a small a and then you make a little arc. This is how you label an angle. OK?

 

[JulianMathHelp]

You have a vertex A. Draw 2 rays from A. You now have an angle. You want to call the angle a. So near the vertex you write a small a and then you make a little arc. This is how you label an angle. OK?

Yes, it is clear I’m obsessing over little things. I ubderstabd it, and thank you for your time.