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

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?

• The link is not working for me. Regardless, though, it is preferable to make questions self-contained, whenever possible. Please edit your question to include relevant excerpts and diagrams. – Cameron Buie Nov 18 '13 at 20:52

## 2 Answers

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.

• Ah, thanks. I knew that inscribed angles could be equal if they mark the same arc, but I didnt know the theorem about the central central angle. – David says Reinstate Monica Nov 18 '13 at 20:56

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