Clock Angles in 5 Seconds: The 30H - 11M/2 Magic Formula!

Given time: 10:10 H = 10, M = 10 Angle = |30H - (11/2)M| Angle = |30 * 10 - (11/2) * 10| Angle = |300 - 11 * 5| Angle = |300 - 55| Angle = |245| Angle = 245° Since 245° is greater than 180°, we need to find the smaller angle: Smaller Angle = 360° - 245° = 115°. Wait, let me recheck my calculation. 300 - 55 = 245. 360 - 245 = 115. None of the options are 115. Let me re-evaluate the options or the question. Ah, I made a mistake in the options or my calculation. Let me correct the options to include 115 or adjust the question/solution to match the options. Let's re-calculate for 10:10. H=10, M=10. |30*10 - (11/2)*10| = |300 - 55| = 245. Smaller angle = 360 - 245 = 115. The options are 145, 155, 160, 170. This means my quiz question or options are flawed. Let me change the quiz question to 9:30. Revised Quiz Question: What is the smaller angle between the hour and minute hands of a clock at 9:30? Revised Quiz Options: [105°, 115°, 125°, 135°] Let's re-calculate for 9:30: H = 9, M = 30 Angle = |30 * 9 - (11/2) * 30| Angle = |270 - 11 * 15| Angle = |270 - 165| Angle = |105| Angle = 105° Since 105° is not greater than 180°, this is the smaller angle. So, the correct option is 105°. This matches option A (index 0). Corrected Quiz Explanation: Given time: 9:30 H = 9, M = 30 Angle = |30H - (11/2)M| Angle = |30 * 9 - (11/2) * 30| Angle = |270 - 11 * 15| Angle = |270 - 165| Angle = |105| Angle = 105° Since 105° is not greater than 180°, this is the smaller angle between the hands.

दिया गया समय: 9:30 H = 9, M = 30 कोण = |30H - (11/2)M| कोण = |30 * 9 - (11/2) * 30| कोण = |270 - 11 * 15| कोण = |270 - 165| कोण = |105| कोण = 105° चूंकि 105° 180° से अधिक नहीं है, यही सुइयों के बीच का छोटा कोण है।