Discover How to Find Angle A in a Regular Pentagon | Angular Proof Assistance

In summary, the conversation discusses the problem of finding angle A in a regular pentagon ABCDE, where A is at the top and C and D form an isosceles triangle at the bottom. Different approaches are suggested, including using the inscribed angle theorem and constructing a line parallel to CD through A. However, since no lengths or other angles are given, it is not possible to determine the exact value of angle A. The conversation also mentions placing the vertices on a circle and using the center to find the relationship between angle COD and angle CAD.
  • #1
cujo_man
2
0
Hi
Here's the problem I'm stuck with. ABCDE is a regular pentagon. Point A is at the top and C and D are the two points at the bottom forming the commonly seen isosceles trianglein the midle. It then asks to find angle CAD (angle A). Since no lengths or other angles are given, can't i just make a line parallel to CD connecting with A.Then i could just do 180 / 5 to find angle A. I'm not sure if that's the way to do it. If anybody could help, thanks a lot.
 
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  • #2
How do you know that all five of the angles at A are equal to each other?
 
  • #3
well, since no angles or lengths are given, there's no way to know. Thats why I'm stuck with this question.
 
  • #4
In that case, try this:

The vertices can be placed on a circle. Label the center of the circle O and construct line segments from O to C and to D. Angle COD is twice angle CAD.

Incidentally, this provides an answer to my earlier question. :)
 
  • #5
It may be useful to go to this site:
http://en.wikipedia.org/wiki/Circle

and look up the "inscribed angle theorem". You've probably already covered it in class. It won't be enough to solve the problem, but it may be the push you need. Keep plugging.

Carl
 

Related to Discover How to Find Angle A in a Regular Pentagon | Angular Proof Assistance

1. What is a regular pentagon?

A regular pentagon is a polygon with five equal sides and five equal angles. It has rotational symmetry and is one of the five regular polygons (along with equilateral triangle, square, regular hexagon, and regular octagon).

2. How can I find angle A in a regular pentagon?

To find angle A in a regular pentagon, you can use the formula A = (180(n-2))/n, where n is the number of sides (in this case, n = 5). This will give you the measure of each angle in the pentagon, and since all angles are equal in a regular pentagon, angle A will be the same as any other angle in the pentagon.

3. What is the angular proof for finding angle A in a regular pentagon?

The angular proof for finding angle A in a regular pentagon involves using the properties of regular polygons and basic geometry concepts. It can be solved using the formula mentioned above, or by dividing the regular pentagon into triangles and using the properties of triangles to find the measure of angle A.

4. Can I find angle A in a regular pentagon without using any formulas?

Yes, you can find angle A in a regular pentagon without using any formulas by dividing the pentagon into triangles and using the properties of triangles to find the measure of angle A. However, using the formula mentioned above can make the process simpler and more efficient.

5. How is finding angle A in a regular pentagon useful?

Finding angle A in a regular pentagon can be useful in various mathematical and real-life situations. It can be used in geometry and trigonometry problems, as well as in constructing regular pentagons for architectural and artistic purposes. It is also an essential concept in understanding rotational symmetry and the properties of regular polygons.

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