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

Answer: (b)

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

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

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: (d)

Angle traced by the hour hand in $6 hours = (360/12 × 6)^o$ = 180°

Answer: (d)

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

∴ Angled traced by hour hand in 8 h 30 min =$[{(8 × 60) + 30}x1/2]^o$

= $[{480 + 30} ×1/2]° = 510 × (1/2)^o = 255°$

Then,  Angle traced by minute hand per minute = 6°

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

Hence, Required angle = (255° - 180°) = 75°

Answer: (b)

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

∴ Angle traced by hour hand in 7 h 35 min = [(7 × 60) + 35] × $1°/2$

= (420 + 35) × 1°/2 = 455 × $1°/2$ = 227 $1°/2$

∴ angle traced by minute hand per minute = 6°

Angle traced by minute hand in 35 min = 35 × 6° = 210°

∴ required angle = 227 1°/2 - 201° = 17$1°/2$

Answer: (a)

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

∴ Angle traced by hour hand in 1 h = 1°/2 × 60 = 30°

Time period between 8 O' clock to 2 O' clock = 6h

∴ angle traced by hour hand in 6h = 30° × 6 = 180°