1. Answer: $15-45$.

Solution. Let's list the beautiful moments of time: 8-04, 8-16, 8-28, 8-40, 8-52, 9-03, 9-15, 9-27, 9-39, 9-51, 10-02, 10-14, 10-26, 10-38, 10-50, 11-01, 11-13, 11-25, 11-37, 11-49, 12-00, 12-12, 12-24, 12-36, 12-48, 13-11, 13-23, 13-35, 13-47, 13-59, 14-10, 14-22, 14-34, 14-46, 14-58, 15-09, 15-21, 15-33, 15-45.
1. Ivan considers the current time beautiful if the sum of hours and minutes is divisible by 12 (for example, 11:13 is a beautiful time, since $11+13=24$ is divisible by 12). Today he woke up at 7:49 and stared at the clock. When will it be the 39th moment of time that Ivan considers beautiful?