Question

At 5:20 the angle formed between the two hands of a clock is

• A. obtuse
• B. right
• C. acute
• D. none of these

Answer 1

The correct option is C acute

A clock is a circle, and a circle always contains ${360}^o$. Since there are

$60$ minutes on a clock, each minute mark is $6^o.$

$\Rightarrow$ $\frac{{360}^o}{60}=6degree$

The minute hand on the clock will point at $20$ minutes, allowing us to calculate it's position on the circle.

$\Rightarrow$ $20minutes\times 6=120degree$

So the angle made by the hour hand in $5$ hours $20$ minutes $=5\frac{1}{3}hours$

$=\frac{16}{3}\times \frac{{360}^o}{12}$

$={160}^o$

Hence angle between the hour hand and minute hand at $5:20={160}^o-{120}^o={40}^o$

$\therefore$ ${40}^o$ is less than ${90}^o$ means its acute angle.

$\therefore$ At $5:20$ the angle formed between the two hands of a clock is $acute.$