Question

The reflex angle between the hands of the clock at $10:25$ is

Answer 1

Step-1: Angle traced by hour hand

According to the question,

A reflex angle is an angle that measures more than ${180}^{\circ }$ and less than ${360}^{\circ }$

On observing the clock we note that the angle between the hands at $10:00=60⁰$

So the hour hand traces

$\frac{{360}^{\circ }}{12}=30⁰\mathrm{per}\mathrm{hour}$ ( As there are $12hours$in a clock and it makes ${360}^{\circ }$)

Angle traced per minute by the hour hand

$\frac{{30}^{\circ }}{60}=0.5^{\circ }\mathrm{per}\mathrm{minute}$ ( As $1hour=60minute$)

Step-2: Find the angle traced by the minute hand

Also, minute hand traces $360⁰$per hour

Angle traced in $1minute=\frac{{360}^{\circ }}{60}=6^{\circ }$

Step-3: Find the reflex angle between the hands of the clock at $10:25$

To find the reflex angle of a given angle, we need to subtract the given measure from ${360}^{\circ }$

Difference of angle traced by the hour hand and minute hand in a minute$=6-0.5=5.5⁰$

So, at $10:25$ the difference between the hands$=60+25\times (5.5)=197.5⁰$

Hence, the reflex angle between the hands of the clock at $10:25$is $197.5⁰$