Question

a clock shows 10:10. what is the smaller angle between the hands (°)? 115° 85° 95° 75° rioju will now pull a fortune...

Explanation:

Step1: Calculate hour - hand position

The hour - hand moves 30 degrees in 1 hour (360÷12 = 30 degrees per hour) and 0.5 degrees in 1 minute (30÷60 = 0.5 degrees per minute). At 10:10, the hour - hand has moved 10 hours and 10 minutes. The position of the hour - hand is \(10\times30+10\times0.5=300 + 5=305\) degrees.

Step2: Calculate minute - hand position

The minute - hand moves 6 degrees in 1 minute (360÷60 = 6 degrees per minute). At 10 minutes, the position of the minute - hand is \(10\times6 = 60\) degrees.

Step3: Calculate the angle between hands

The angle between the hands is \(|305 - 60|=245\) degrees. But we want the smaller angle, and since the full - circle is 360 degrees, the smaller angle is \(360−245 = 115\) degrees.

Answer:

115°