diff --git a/masque/builder/utils.py b/masque/builder/utils.py
index c466c71..6e3334d 100644
--- a/masque/builder/utils.py
+++ b/masque/builder/utils.py
@@ -21,7 +21,7 @@ def ell(
         *,
         spacing: float | ArrayLike | None = None,
         set_rotation: float | None = None,
-        ) -> dict[str, float]:
+        ) -> dict[str, numpy.float64]:
     """
     Calculate extension for each port in order to build a 90-degree bend with the provided
     channel spacing:
diff --git a/masque/shapes/arc.py b/masque/shapes/arc.py
index 67d932d..4b69dbb 100644
--- a/masque/shapes/arc.py
+++ b/masque/shapes/arc.py
@@ -233,7 +233,7 @@ class Arc(Shape):
         r0, r1 = self.radii
 
         # Convert from polar angle to ellipse parameter (for [rx*cos(t), ry*sin(t)] representation)
-        a_ranges = cast(tuple[tuple[float, float], tuple[float, float]], self._angles_to_parameters())
+        a_ranges = cast(_array2x2_t, self._angles_to_parameters())
 
         # Approximate perimeter via numerical integration
 
@@ -286,6 +286,7 @@ class Arc(Shape):
                 thetas = thetas[::-1]
             return thetas
 
+        thetas_inner: NDArray[numpy.float64]
         if wh in (r0, r1):
             thetas_inner = numpy.zeros(1)      # Don't generate multiple vertices if we're at the origin
         else:
@@ -320,7 +321,7 @@ class Arc(Shape):
 
         If the extrema are innaccessible due to arc constraints, check the arc endpoints instead.
         """
-        a_ranges = self._angles_to_parameters()
+        a_ranges = cast(_array2x2_t, self._angles_to_parameters())
 
         mins = []
         maxs = []
@@ -431,7 +432,7 @@ class Arc(Shape):
              [[x2, y2], [x3, y3]]],    would create this arc from its corresponding ellipse.
             ```
         """
-        a_ranges = self._angles_to_parameters()
+        a_ranges = cast(_array2x2_t, self._angles_to_parameters())
 
         mins = []
         maxs = []
@@ -479,3 +480,5 @@ class Arc(Shape):
         angles = f' a°{numpy.rad2deg(self.angles)}'
         rotation = f' r°{numpy.rad2deg(self.rotation):g}' if self.rotation != 0 else ''
         return f'<Arc o{self.offset} r{self.radii}{angles} w{self.width:g}{rotation}>'
+
+_array2x2_t = tuple[tuple[float, float], tuple[float, float]]
diff --git a/masque/shapes/path.py b/masque/shapes/path.py
index a53b5c7..717e59f 100644
--- a/masque/shapes/path.py
+++ b/masque/shapes/path.py
@@ -271,7 +271,7 @@ class Path(Shape):
         # TODO: Path.travel() needs testing
         direction = numpy.array([1, 0])
 
-        verts = [numpy.zeros(2)]
+        verts: list[NDArray[numpy.float64]] = [numpy.zeros(2)]
         for angle, distance in travel_pairs:
             direction = numpy.dot(rotation_matrix_2d(angle), direction.T).T
             verts.append(verts[-1] + direction * distance)