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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°** .

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Minute hand covers $360^o$ in $60$ minutes.

Hour hand covers $360^o$ in $12 \times 60=720$ minutes

$\therefore $ In $1$ minute hour hand and minute hand covers $6^o$ and $0.5^o$ respectively.

Now At $2:00$ angle difference = $60^o$

and relative difference$=5.5^o$

$\therefore $ At $2:30$ difference $ = 30 \times 5.5-60=\color{Red}{105^o}$

Hour hand covers $360^o$ in $12 \times 60=720$ minutes

$\therefore $ In $1$ minute hour hand and minute hand covers $6^o$ and $0.5^o$ respectively.

Now At $2:00$ angle difference = $60^o$

and relative difference$=5.5^o$

$\therefore $ At $2:30$ difference $ = 30 \times 5.5-60=\color{Red}{105^o}$

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