Find the measure of the angle swept by the hour hand between noon and 1:45

let's recall that a circle has a total of 360°, and the circular clock has 60 minutes ticks.

if there are 360° in the clock then each minute tick has an angle of 360/60 = 6°.

from 12pm to 1pm is 1 whole hour, or 60 minutes, namely 360°.

from 1pm to 1:45pm is 45 minutes, and therefore 6°*45 = 270°.

so the minute hand went through 360° + 270° = 630°.