# Circle and Polygon Properties

## Homework Statement

http://i41.tinypic.com/35mno6v.jpg

2. The attempt at a solution
So far, I found out that angle 4 and 5 is 55, because angle D is 110.. but I don't know if that's right. Please help!

## Answers and Replies

Mark44
Mentor
Angle BDA is 110 degrees, because angle 1 is 70 degrees. Angles 4 and 5 are equal, because triangle BDA is isosceles. Angles 4, 5 and BDA have to add to 180 degrees, which they don't do if angles 4 and 5 are 55 degrees each.

What about angle 2 and 3? My answer was 55 for both of them..

Mark44
Mentor
Those would be correct if triangle BCD is isosceles, with BD = CD. Can you establish that equality somehow?

Hmm, I suppose I can't. Now I've hit the bricks, I don't know how to figure it out.

Mark44
Mentor
Is there any other information given in this problem, such as at the top of the set of problems?

One thing I haven't used is the statement that AB is tangent at B. I don't understand why this is significant or how it ties into this problem.

Once you have angle 4/5 you can easily figure out 2 using inscribed angles and angles formed by tangents.

One thing I haven't used is the statement that AB is tangent at B. I don't understand why this is significant or how it ties into this problem.

It is significant because an angle formed by a chord and a tangent to a circle is half the arc it intercepts. Angles 2 and 4 are inscribed angles that intercept the same arc, so they are congruent.