How does this proof of law of sines determine equal angles?

Question

I was reading over this proof of the law of sines and they say that $\angle CAB = \angle DOB$ because of "basic geometry". I do not get it though, how can you say that the angles are equal?

Answer 1

I think it is referring to a property of inscribed angles:

The measure of the intercepted arc (equal to its central angle) is exactly twice the measure of the inscribed angle.

So $m\angle COB = 2 m\angle CAB$, and they bisected segment $CB$ to halve the angle.

Answer 2

$\angle CAB$ is an inscribed angle; $\angle DOB$ is half of a central angle through the same arc, so the angles are equal.

See http://www.mathopenref.com/arccentralangletheorem.html for more.