Find the angle between the hour and minute hands at 6:30 a.m.

Introduction / Context:
We compute the smaller angle between the hour and minute hands at a specified time.

Given Data / Assumptions:

• Time: 6:30 a.m.
• Minute hand speed: 6 degrees per minute.
• Hour hand speed: 0.5 degrees per minute.

Concept / Approach:
The minute hand angle from 12 at t minutes is 6t. The hour hand angle at h:t is 30h + 0.5t. The absolute difference gives the angle; choose the acute one if two are possible.

Step-by-Step Solution:
At 6:30, minute angle = 6 * 30 = 180°.Hour angle = 30*6 + 0.5*30 = 180 + 15 = 195°.Difference = |195 − 180| = 15°.

Verification / Alternative check:
General formula for angle at h:m is |30h − 5.5m|; substituting 6:30 → |180 − 165| = 15°, matches.

Why Other Options Are Wrong:
22.5° is the angle between hour positions at quarter intervals in some cases, not here. 25° is arbitrary. “None of these” is unnecessary since 15° fits.

Common Pitfalls:
Forgetting the hour hand advances between hours (the 0.5m term).

Final Answer:
15°