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

[cujo_man]

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.

 

[Tide]

How do you know that all five of the angles at A are equal to each other?

 

[cujo_man]

well, since no angles or lengths are given, there's no way to know. Thats why I'm stuck with this question.

 

[Tide]

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. :)

 

[CarlB]

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