Question

What is the Reflex angle between two hands of a clock at 10:25?

Hint:

Always be careful whether the question asks for the standard angle or the reflex angle. If the calculated angle is \(\theta\), the reflex angle is always 360\(^{\circ}\) - \(\theta\).

Answer 1

Correct Answer: 197.5

Step 1: Understanding the Question:
We need to find the reflex angle between the hour and minute hands at 10:25. A reflex angle is an angle greater than 180\(^{\circ}\) and less than 360\(^{\circ}\). First, we'll find the smaller angle and then subtract it from 360\(^{\circ}\).
Step 2: Key Formula or Approach:
The formula to find the angle (\(\theta\)) between the hour hand (H) and the minute hand (M) is: \[ \theta = \left| 30H - \frac{11}{2}M \right| \] Step 3: Detailed Explanation:
Given time is 10:25, so H = 10 and M = 25.
Substitute these values into the formula: \[ \theta = \left| 30(10) - \frac{11}{2}(25) \right| \] \[ \theta = \left| 300 - \frac{275}{2} \right| \] \[ \theta = \left| 300 - 137.5 \right| \] \[ \theta = 162.5^{\circ} \] This is the smaller angle between the hands. The reflex angle is the other angle that makes up the full circle.
Reflex Angle = 360\(^{\circ}\) - \(\theta\)
\[ \text{Reflex Angle} = 360^{\circ} - 162.5^{\circ} \] \[ \text{Reflex Angle} = 197.5^{\circ} \] Step 4: Final Answer:
The reflex angle between the hands of a clock at 10:25 is 197.5\(^{\circ}\).