I don't understand how to find the measure of angle DAB in this

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One way to do it.

Find the center of the circle, label it. I suggest labeling it "O". I assume you know that OA is perpendicular to AD (if you don't, find out why, interesting proof). Now drop a perpendicular to B from AD. Label the point on AD where the perpendicular from B lands as G. Then we know that

m GAB + m ABG = 90 and m GAB = m DAB

Again I assume you know why? Ask if you don't. So all we need to know is m ABG.

By an argument based on parallel lines, m ABG = m BAO

Because triangle BAO is isosceles, m BAO = m OBA and m AOB = 180 - 2 m BAO.

This means if I know m AOB, I can figure out m BAO then ABG then GAB = DAB.

So what is m AOB? They tell you in the diagram.

See the attachment, a GSP diagram. If you don't have GSP or a similar program, you might consider buying it. A little costly. You can get Geogebra 4.2 for free, and it's pretty good, in some ways better than GSP imho.

the angle bttween a tangent and chord is 1/2 of the chord arc.Answer is 70