How Do Tangents and Chords Affect Angles in Circles?

[Turquoise]

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!

 

[Mark44]

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.

 

[Turquoise]

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

 

[Mark44]

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

 

[Turquoise]

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

 

[Mark44]

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.

 

[LunaEques]

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

 

[meiso]

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.