Exact angle between clock hands at 10:10 — Compute the smaller angle between the hour and minute hands at 10:10 am.

Introduction / Context:
This exercise reinforces computing absolute angles for each hand and then selecting the smaller separation. Options may include the reflex angle (greater than 180°) to test whether you know to choose the smaller angle by default unless otherwise stated.

Given Data / Assumptions:

• Time: 10:10.
• Hour-hand angle = 30 × H + 0.5 × M.
• Minute-hand angle = 6 × M.

Concept / Approach:
Compute positions and then the difference. If the difference exceeds 180°, subtract from 360° to get the smaller angle. Provide the exact value rather than rounding to a listed distractor.

Step-by-Step Solution:
Hour-hand angle: 30 × 10 + 0.5 × 10 = 300 + 5 = 305°.Minute-hand angle: 6 × 10 = 60°.Raw difference: |305 − 60| = 245°.Smaller angle: 360° − 245° = 115°.

Verification / Alternative check:
At 10:10 the hands are a bit more than a quarter-turn apart, consistent with ~115° rather than the reflex 245°.

Why Other Options Are Wrong:
245° is the reflex angle; 195° and 175° are incorrect alternatives. Thus “None of these” is correct.

Common Pitfalls:
Choosing the reflex angle when the question asks for “the angle between,” which conventionally means the smaller angle.

Final Answer:
None of these (correct smaller angle = 115°)