We want to find m∠ ABD . We know that if a secant and a tangent intersect at the point of tangency, then the measure of the each angle formed is one half the measure of the intercepted arc.
m∠ ABD = 1/2(mBCD)
Note that arcs BCD and DB form together a full turn around the origin. By the Arc Addition Postulate, we can write an expression for mBCD and use it to find m∠ ABD.
mBCD = 360^(∘) - mDB
↓
m∠ ABD = 1/2(360^(∘) - mDB)
Let's substitute the known value for mDB and solve it for m∠ ABD.
