Is there a relationship between degrees of angles in a polygon to it's diagonals?

shahar

Full Member
Joined
Jul 19, 2018
Messages
496
Is there a relationship between degrees of angles in a polygon to it's diagonals?
What is the relationship between the degrees of angles in a polygon to diagonals of that polygon?!
 
Is there a relationship between degrees of angles in a polygon to it's diagonals?
What is the relationship between the degrees of angles in a polygon to diagonals of that polygon?!

Are you asking about a relationship between the measure of each interior angle of a regular polygon, and the number of diagonals of that polygon? Or something else, like the sum of the measures of the angles, and something about the lengths of diagonals or angles between them?

If it's the former, then each quantity is related to the number of vertices, so there is an indirect relationship between them. Do you know these two relationships?
 
Are you asking about a relationship between the measure of each interior angle of a regular polygon, and the number of diagonals of that polygon? Or something else, like the sum of the measures of the angles, and something about the lengths of diagonals or angles between them?

If it's the former, then each quantity is related to the number of vertices, so there is an indirect relationship between them. Do you know these two relationships?
I ask if there is connection between angle to diagonals in polygon...
If I draw the all diagonals, is the are relationship between the angles they create to the number of diagonals?
 
I ask if there is connection between angle to diagonals in polygon...
If I draw the all diagonals, is the are relationship between the angles they create to the number of diagonals?

I'm sorry, but you are still not quite being clear! You refer to the "the angles [the diagonals] create"; does that mean the number of intersections of diagonals, or to the measures of [some of] the angles diagonals make [with one another, or with the sides], or what? I understand that by "diagonals" you mean "number of diagonals"; but does that mean "angles" means "number of angles"? I'm sure you are aware that the diagonals "create" many different angles.

Also, I don't think you've ever said whether you are referring only to regular polygons, or not.

It is often necessary to use more words than you think, in order to fully state what you mean.

Now, if you mean "is there a relationship between the measures of the angles between sides of a regular polygon, and the number of diagonals, then I already said yes, because both are related to the number of sides. That was part of what you quoted.
 
I'm sorry, but you are still not quite being
Now, if you mean "is there a relationship between the measures of the angles between sides of a regular polygon, and the number of diagonals, then I already said yes, because both are related to the number of sides. That was part of what you quoted.
What the differences between regular polygon to non-regular polygon?
Why is it important to emphasize the differences to answer my question?
Again:
My question is there a relationships between angles to diagonals in polygon when the diagonals that come out from the angle [diagonal of this angle]...?
 
Seriously? A "regular polygon" is a polygon in which all sides are the same length and all angles the same measure. A square is a regular polygon. Non-square rectangles and rhombi are non-regular polygons. In a square, a "regular quadrilateral", diagonals make 45 degree angles with the sides and intersect at right angles. In a "non-regular quadrilateral" those angles can be anything from almost 0 to almost 90 degrees.
 
What the differences between regular polygon to non-regular polygon?
Why is it important to emphasize the differences to answer my question?
Again:
My question is there a relationships between angles to diagonals in polygon when the diagonals that come out from the angle [diagonal of this angle]...?

Please, either say that my rewording is correct, or give your own precise wording. As it is, I'm not at all sure you yourself know what you want. Now you seem to be asking about the angles between diagonals at a particular vertex of the polygon. (There is no such thing as "the diagonal of an angle". And, in general, each angle might be different.

But if you are asking only about regular polygons (all sides equal, all angles equal), then it turns out that all angles between diagonals at a vertex are equal. If you know the theorem relating angles inscribed in a circle and the arcs they cut off, you can calculate what this angle is.

If that doesn't answer your question, how about giving an example? Show me a polygon and point out exactly what you want to know about it -- what angles, whether it is their values or the number of them, and so on. Examples are a great help in communication when you don't have the words to say what you want, and the other person doesn't know your context.
 
What the differences between regular polygon to non-regular polygon?
Why is it important to emphasize the differences to answer my question?
Again:
My question is there a relationships between angles to diagonals in polygon when the diagonals that come out from the angle [diagonal of this angle]...?
The problems with your question are (1) your English is poor, and (2) your question is grossly under-specified.

Yes, there are relationships among the angles of a pentagon and its diagonals. For example, the ratio of distinct interior angles to distinct diagonals is exactly 1 : 1.

If you have a specific question, please formulate it with sufficient specificity in the best English you can muster.

EDIT: There was an error in my original text that I failed to catch when proofing. I have corrected it. Apologies to all who were confused by my error.
 
Last edited:
I'm sorry, but you are still not quite being clear! You refer to the "the angles [the diagonals] create"; does that mean the number of intersections of diagonals, or to the measures of [some of] the angles diagonals make [with one another, or with the sides], or what? I understand that by "diagonals" you mean "number of diagonals"; but does that mean "angles" means "number of angles"? I'm sure you are aware that the diagonals "create" many different angles.

Now, if you mean "is there a relationship between the measures of the angles between sides of a regular polygon, and the number of diagonals, then I already said yes, because both are related to the number of sides. That was part of what you quoted.
I substitute the expression "regular polygon" by the two words that I think I realize from it: "concave" and "convex".
So, now when it clear to me. [The term regular polygon].
How the diagonals of one angle that in concave polygon different from angle convex polygon?
(A) When they the same?...
(B) When they different?...
It there a way to know more information about the diagonals by those two types of polygon?
 
English problems

Please, either say that my rewording is correct, or give your own precise wording. As it is, I'm not at all sure you yourself know what you want. Now you seem to be asking about the angles between diagonals at a particular vertex of the polygon. (There is no such thing as "the diagonal of an angle". And, in general, each angle might be different.

But if you are asking only about regular polygons (all sides equal, all angles equal), then it turns out that all angles between diagonals at a vertex are equal. If you know the theorem relating angles inscribed in a circle and the arcs they cut off, you can calculate what this angle is.

If that doesn't answer your question, how about giving an example? Show me a polygon and point out exactly what you want to know about it -- what angles, whether it is their values or the number of them, and so on. Examples are a great help in communication when you don't have the words to say what you want, and the other person doesn't know your context.
Question 2:
I don't understand the underline text that is quoted?
 
An angle is "inscribed in a circle" if its vertex lies on the circle and both rays go through the interior of the circle. That angle "cuts off" the arc of the circle that lies between the rays. Circular arcs can be measured like angles in degrees or radians. That measure is the same as the measure of the "central angle", the angle with vertex at the center of the circle. The theorem Dr, Peterson refers to says that the measure of an angle inscribed in a circle is half the measure of the arc cut off by that angle.


For example, draw a circle and then draw a horizontal line from the center of the circle to the right and draw a vertical line from the center upward. (Say the unit circle centered at (0, 0) with the positive x-axis and positive y-axis as the horizontal and vertical rays. Those rays cut the circle at (1, 0) and (0, 1)) Those rays make a right angle so cut off an arc with measure 90 degrees (\(\displaystyle \pi/2\) radians). The angle formed by drawing rays from another point on the circle through (1, 0) and (0, 1) has measure 90/2= 45 degrees (\(\displaystyle \pi/4\) radians).
 
Last edited:
I substitute the expression "regular polygon" by the two words that I think I realize from it: "concave" and "convex".
So, now when it clear to me. [The term regular polygon].
How the diagonals of one angle that in concave polygon different from angle convex polygon?
(A) When they the same?...
(B) When they different?...
It there a way to know more information about the diagonals by those two types of polygon?

A regular polygon is one whose sides are all equal, and whose angles are all equal. That is the meaning of the term.

Any regular polygon is convex, but not all convex polygons are regular. Your question is probably only about regular polygons, not about any convex polygon. It will not be helpful to bring in the latter concept here.

I don't think you've ever told us why you are asking this question. If you told us the context, we could determine what conditions are important in your question, and interpret what you are asking for. Please, please help us by telling us these missing details.
 
Cut off

What the meaning of expression "cut off"... an angle...
 
What the meaning of expression "cut off"... an angle...
Nothing has been said here about "cutting off" an angle. What has been said is an angle "cutting off" an arc. And I have already explained that: "That angle "cuts off" the arc of the circle that lies between the rays."
 
The problems with your question are (1) your English is poor, and (2) your question is grossly under-specified.

Yes, there are relationships among the angles of a pentagon and its diagonals. For example, the ratio of distinct interior angles to distinct diagonals is exactly 1 : 2.

If you have a specific question, please formulate it with sufficient specificity in the best English you can muster.
I don't understand the underline text...
Can you show a picture or image or something...
 
Here is a picture of what I think you have been asking about:
FMH112667.png
This is a polygon with n = 7 sides. There are n-2 = 5 angles at A, all of which are equal (congruent) because they are inscribed angles that "cut off" equal arcs on the circumference of the circle containing the polygon. So if you have learned the formula for the interior angles of a regular polygon, you can just divide by n-2 to get a formula for each of these angles.

Is this what you wanted? If so, a picture would have helped you ask the question clearly.
 
Is this what you wanted? If so, a picture would have helped you ask the question clearly.
I don't understand what ratio the second forum member describe in his post.
What is the ratio?
Where is it found?
Is it exist in other polygon? Why Yes? Why Not?
What is the proof that show it? (a link will be helpful!)
I quote the context of my question:
For example, the ratio of distinct interior angles to distinct diagonals is exactly 1 : 2.
 
I don't understand what ratio the second forum member describe in his post.
What is the ratio?
Where is it found?
Is it exist in other polygon? Why Yes? Why Not?
What is the proof that show it? (a link will be helpful!)
I quote the context of my question:
For example, the ratio of distinct interior angles to distinct diagonals is exactly 1 : 2.

You're referring to what JeffM said in post #10, right?

I have no idea what he meant. A pentagon has 5 vertices, therefore 5 interior angles, and 5 diagonals, so if he meant the ratio of the number of interior angles to the number of diagonals, that's 1:1. It would be different for other polygons. But is this ratio what you were asking about? I still don't think we know what you are asking for!
 
Top