图中显示了一个正六边形 ABCDEF 和一个正五边形 EFGHI。 求 ∠EDI。

1. Find the angle $\angle DEI$ at the common vertex $E$.

For the regular hexagon, $\angle DEF = 120^\circ$.

For the regular pentagon, $\angle FEI = 108^\circ$.

Angles around point $E$ add up to $360^\circ$, so
$\angle DEI = 360^\circ - 120^\circ - 108^\circ = 132^\circ.$

2. Use the isosceles triangle property in triangle $DEI$.

Since $DE$ is a side of the regular hexagon and $EI$ is a side of the regular pentagon, and both share side $EF$,
$DE = EF = EI.$

Hence triangle $DEI$ is isosceles, so
$\angle EDI = \angle DIE.$

Therefore
$\angle EDI = \frac{180^\circ - 132^\circ}{2} = 24^\circ.$