The measure of a dihedral angle is defined as the measure of the angle which is the intersection of the dihedral angle with a plane perpendicular to its edge. This definition makes sense, because it is easy to prove that all such angles are congruent among them.
Angles whose sides are not perpendicular to the dihedral edge are, in general, different. Let $AB$ and $CB$ be perpendicular at $B$ to the edge; if $\theta=\angle ABC$ then from the cosine law we have (see diagram below):
$$
\cos\theta={AB^2+BC^2-AC^2\over2\,AB\cdot BC}.
$$
Let now $AD$ be parallel to the edge and $\phi=\angle DBC$.
Notice that $AD$ is perpendicular to plane $ABC$,
hence $AD\perp AC$ and $AD\perp AB$.
From the cosine law we have:
$$
\cos\phi={DB^2+BC^2-DC^2\over2\,DB\cdot BC}.
$$
But $DC^2=AC^2+AD^2$ and $DB^2=AB^2+AD^2$, hence:
$$
\cos\phi={AB^2+BC^2-AC^2\over2\,DB\cdot BC}={AB\over DB}\cos\theta.
$$
If follows that $|\cos\phi|<|\cos\theta|$, unless $\cos\theta=0$, i.e. $\theta=90°$.
