When the clock shows time 5:20, the angle formed between the two hands is

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Obtuse

Right

Acute

None of these

answer is C.

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Detailed Solution

A clock is a circle, and a circle always contains 360

°

. Since there are 60 minutes on a clock, each minute mark is 6

° .

Then,

\frac{360 °}{60} 6 degree

The minute hand on the clock will point at 20 minutes, allowing us to calculate it's position on the circle.
Then, 20minutes×6=120degree
So, the angle made by the hour hand in 5 hours 20 minutes =

5 \frac{1}{3}

\frac{16}{3} \times \frac{360 °}{12}

=160

°

Hence angle between the hour hand and minute hand at 5:20=160

°

−120

°

=40

°

So, 40

°

is less than 90

°

means its acute angle.
Then, At 5:20 the angle formed between the two hands of a clock is acute.
Hence option (3) is the correct answer.

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