cd←→ is tangent to circle a at point b.

what is the measure of ∠abd?

45º

60º

90º

180º

By definition the tangent to a circle is a line that touches/intersects the circle at only ONE point and should be the closest point ON THE LINE to the center of the circle.

Now, let us take an example of ABD triangle. As you can see it is a right angled triangle, where: AD2=AB2+BD2 , and the angle ∠ABD has to be 90° because ABD is a right angled triangle(mentioned above).

Also, tangents to the circle ALWAYS make 90° angle to the radius of the circle.

So the correct answer = 90°.