The entire clock is a circle. So, it is made up of 360°.The clock is divided into 12 sections and each section or each number represents an angle and the separation between them is (360°/12) = 30°.
At 2:30 the minute hand points to the 6 and the hour hand points halfway between the 2 and the 3.
The angle between the halfway of 2 and 3 is = 1/2 x 30° = 15°.
The angle between 3 and 4 is 30°.
The angle between 4 and 5 is 30°.
The angle between 5 and 6 is 30°.
So, The angle between hands of clock at 2:30 pm is = ( 15° + 30° + 30° +30° ) = 105° .