Ninety degrees

[JPablo]

He’s got himself ninety degrees convinced that he’s part of the physical universe...

ninety degrees: referring to one quarter of the whole of something; from a ninety degree angle, that is, the angle formed by two lines that are perpendicular to each other and is one fourth of a circle of 360 degrees.

Do you think that this definition applies to my sentence?

or is it rather... :?:

He’s got himself perpendicularly (straight up and down; fully) convinced that he’s part of the physical universe... :?:

[Rusty]

I've never heard this phrase used. Since 90 degrees is a quarter of a circle, I would favor 'a quarter convinced' as a suitable alternative. However, 'half convinced' is more common, and I can't totally rule it out as a possible meaning of the phrase. Since 360 degrees make a complete circle, I wouldn't think 'fully convinced' equals 'ninety degrees convinced'.

[JPablo]

Thank you, Rusty. What you say makes sense.