Copyright © University of Cambridge. All rights reserved.
'Handy Angles' printed from https://nrich.maths.org/
Let $x$ denote the angle between the hour hand and the vertical,
and $y$ the angle between the minute hand and the vertical.
$\frac{360}{12}=30$ so we calculate that $x = \left( 4+\frac{2}{3}
\right) \times 30 =140^\circ$ and $y = 8 \times 30 = 240^\circ$.
The angle between the hands is $y - x = 240^\circ - 140^\circ =
100^\circ$.