The larger angle between the hands of a clock at 10:30am. is

Answer 1

75 degrees.

To find the angle between the hands of a clock at a specific time, we use the following formula:

Angle = |(30H - 11/2M)|

where H is the hour (in 12-hour format) and M is the minute.

For 10:30am, H = 10 and M = 30. Plugging these values into the formula, we get:

Angle = |(30 x 10 - 11/2 x 30)|
= |(300 - 165)|
= 135 or 225 degrees

However, we need to take into account that the minute hand is only halfway between the 10 and 11 on the clock face. This means that the hour hand has moved a little past the 10 o'clock mark, creating a smaller angle between the hands.

To find this smaller angle, we need to subtract the angle covered by the hour hand from the total angle calculated above. The hour hand moves 30 degrees for every hour, or 0.5 degrees for every minute. At 10:30am, the hour hand has covered:

0.5 x (10 x 60 + 30) = 0.5 x 630 = 315 degrees

Subtracting this from the total angle, we get:

Angle = 225 - 315 = -90

This is a negative angle, which means that we have gone past the 12 o'clock mark and need to add 360 degrees to get the positive value:

Angle = -90 + 360 = 270 degrees

Therefore, the larger angle between the hands of a clock at 10:30am is 270 degrees.