Can time be measured in degrees?

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As far as I know, minutes and seconds (units of time) are definitely somehow related to the angular conversions we study in high school math (1 degree = 60 minutes, so on and so forth). So why don't we measure time in degrees (or even radians)? Are these minutes in a clock even related to these conversions taught in trigonometry class? And, how are earth's latitudes measured in degrees, I mean latitudes are straight lines and I don't see any angle forming. I'm literally at sixes and sevens right now, please provide me with some insight on this.

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Lines of latitude aren't straight lines (even if we interpret "straight line" as "geodesic"); they're circles. The latitude of a point is the the angle made by the pair of rays from the centre of the earth to the point and to a point at the same longitude on the equator.