Multiple choice

At what time between $5$ and $5:30$ the hands of a clock will make an angle of $18^{\circ}.$

  1. $12$ minutes past $5$
  2. $24$ minutes past $5$
  3. $36$ minutes past $5$
  4. $40$ minutes past $5$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Angle = |30H - 5.5M|. 18 = |30(5) - 5.5M| => 18 = |150 - 5.5M|. Case 1: 150 - 5.5M = 18 => 5.5M = 132 => M = 24. Case 2: 5.5M - 150 = 18 => 5.5M = 168 => M = 30.54. 24 minutes past 5 is the correct answer.

AI explanation

Using the clock angle formula for degrees, we solve (30 * 5 - 11/2 * M) = 18 to find the minutes. This simplifies to 150 - 5.5M = 18, so 5.5M = 132, which gives M = 24. Therefore, the hands make an angle of 18 degrees at 24 minutes past 5.

Keep practicing — related questions