A video call starts at the time shown. At what time after this will the two hands first point in exactly opposite directions?

At 1:00 the minute hand is $30^{\circ }$ behind the hour hand; to be opposite it must be $180^{\circ }$ ahead, a gain of $210^{\circ }$ at $5.5^{\circ }$ per minute: $\frac{210}{5.5}=38\frac{2}{11}$ min past 1, after the 1:10 shown. (35 min ignores the hour hand's motion; $21\frac{9}{11}$ is a right angle.)