Assume that the hands of a clock move continuously across its face. What are the times, if any, between 4 and 5 p. m. at which its hands form an angle of 144°?

At 4:48 p. m.

Step-by-step explanation:

angle between hands of the clock is given by

θ = | 30H - 11/2M |

Where H and M are hours and minutes respectively.

H=4

θ = | 30*4 - 11/2M |

⇒144° = | 120 - 11/2M |

solving Above equation we get M = 48 minutes

Time = 4:48 p. m.

therefore between 4 and 5 p. m. at 4:48 p. m. the angle between minute and hour hand is 144°