Geometry Foundation Quiz #1 Q10 Angle

[user4648]

Hi,

I have a question, maybe it’s very obvious, but I’m unable to see it.

How is the upper angles 90 degrees? In Greg’s explanation, he said that whenever you have a diameter, then that angle equals 90 degrees. Investigating further, I found it’s part of Thale’s theorem. Is there a lesson in Prepswift where he talks about this theorem? I couldn’t find it. Or where in his videos does he mention this?

I would appreciate any answer.

Thank you very much.

[cylverixxx]

AB is the diameter, so the “lower arc” has measure of 180^{\circ}. By the Inscribed Angle Theorem, the measure of the inscribed angle \angle ACB must be half of that.