type 1 angle between the hands of clock Detailed Explanation And More Example

Answer: (b)

Angle traced by hour hand in $13/3 hrs = (360/12 × 13/3)^o= 130°$

Angle traced by min. hand in $20 min = (360/60 × 20)^o = 120°$

∴ Required angle = (130° - 120°) = 10°

Answer: (c)

∴ Angle traced by hour hand per minute = $(1/2)^o$

∴ Angle traced by hour hand in 9 h 30 min

= [(9 × 60) + 30] × $1°/2$ = 570 × $1°/2$ = 285°

∴ angle traced by minute hand per minute = 6°

∴ angle traced by minute hand in 30 min = 30 × 6° = 180°

∴ required angle = (285° - 180°) = 105°

Answer: (c)

∴ Angle traced by hour hand per minute = $(1/2)^o$

&there4 Angle traced by hour hand in 12 h 55 min (i.e., at 0 : 55) = $55 × 1°/2 = 27 1°/2$

&there4 angle traced by minute hand per minute = 6°

Therefore traced by minute hand in 55 min = 55 × 6° = 330°

Therefore required angle = $360° - (330° - 27 1°/2) = 360° + 27 1°/2 - 330°$

$= 387 1°/2 - 330° = 57 1°/2$

Answer: (a)

(A) Angle traced by hour hand in$ 7/6 hrs = (360/12 × 7/6)^o = 35°$

Angle traced by minute hand in $10 min = (360/60 × 10)^o = 60°$

∴ Required angle = (60° - 35°) = 25°

(B) Angle traced by hour hand in $9/4 hrs = (360/12 × 9/4)^o = 67 1°/2$

Angle traced by minute hand in $15 min = (360/60 × 15)^o = 90°$

∴ Required angle = $(90° - 67 1°/2) = 22 1°/2$

(C) Angle traced by hour hand in $26/3 hrs = (360/12 × 26/3)^o = 260°$

Angle traced by minute hand in $40 min = (360/60 × 40)^o$ = 240°

∴ Required angle = (260° - 240°) = 20°

Answer: (b)

Clearly, the minute hand traverses 65 minutes in 1 hour.

∴ Required angle = $(360/60 × 65)^o = 360°$ 

Answer: (c)

Angle traced by hour hand in 21/4 hrs =$ (360/12 × 21/4)^o = 157 1°/2$

Angle traced by min. Hand in 15 min = $(360/12 × 15)^o = 90°$

∴ Required angle = $(157 1°/2) - 90° = 67 1°/2$.