Find an angle

[DukiMath]

On the picture are A, B, C, D on a circle. Chord AB is diameter of the circle . The angle ABC is 35. What is the value of the angle BDC?

 

[DukiMath]

I just see that angles ADB and ACB are 90 degrees and cannot see anything after .

 

[Dr.Peterson]

Draw in segment AC and label angles.

Or, think about the measures (central angles) of arcs AC and BC.

 

[Steven G]

What are the measures of arc AC, arc CB and arc ACB? That should help.

 

[DukiMath]

There is no information about the lenght of the arcs. Just the angles. I am trying different ways but cannot figure it out.

 

[DukiMath]

But i can find them.

 

[Steven G]

There is no information about the lenght of the arcs. Just the angles. I am trying different ways but cannot figure it out.

True, but you can figure them out. After all they did not give you the value of the unknown angle yet you can figure it out.

AB is a diameter, so what is the measure of the arc it cuts off?

Angle ABC is 35, so what is the measure of the angle it cuts off?

After labeling the measure of the two arc above you should know the measure of arc CB. Now what is the measure of angle ?

 

[DukiMath]

i found out that the arc above is 110 and the needed angle 55. Thanks!