We want to find m∠ DAB . 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∠ DAB = 1/2(mDCA)
Note that arcs DCA and AD form together a full turn around the origin. By the Arc Addition Postulate, we can write an expression for mDCA and use it to find m∠ DAB.
mDCA = 360^(∘) - mAD
↓
m∠ DAB = 1/2(360^(∘) - mAD)
Let's substitute the known value for mAD and solve it for m∠ DAB.
