diff --git a/doc/api/api_changes/2017-02-10-DS_elliptical_arc_angle.rst b/doc/api/api_changes/2017-02-10-DS_elliptical_arc_angle.rst
@@ -0,0 +1,8 @@
+Elliptical arcs now drawn between correct angles
+````````````````````````````````````````````````
+
+The `matplotlib.patches.Arc` patch is now correctly drawn between the given
+angles.
+
+Previously a circular arc was drawn and then stretched into an ellipse,
+so the resulting arc did not lie between *theta1* and *theta2*.
diff --git a/lib/matplotlib/patches.py b/lib/matplotlib/patches.py
@@ -1554,8 +1554,6 @@ def __init__(self, xy, width, height, angle=0.0,
         self.theta1 = theta1
         self.theta2 = theta2
 
-        self._path = Path.arc(self.theta1, self.theta2)
-
     @allow_rasterization
     def draw(self, renderer):
         """
@@ -1607,15 +1605,25 @@ def draw(self, renderer):
 
         self._recompute_transform()
 
-        # Get the width and height in pixels
         width = self.convert_xunits(self.width)
         height = self.convert_yunits(self.height)
+
+        # If the width and height of ellipse are not equal, take into account
+        # stretching when calculating angles to draw between
+        def theta_stretch(theta, scale):
+            theta = np.deg2rad(theta)
+            x = np.cos(theta)
+            y = np.sin(theta)
+            return np.rad2deg(np.arctan2(scale * y, x))
+        theta1 = theta_stretch(self.theta1, width / height)
+        theta2 = theta_stretch(self.theta2, width / height)
+
+        # Get width and height in pixels
         width, height = self.get_transform().transform_point(
             (width, height))
         inv_error = (1.0 / 1.89818e-6) * 0.5
-
         if width < inv_error and height < inv_error:
-            # self._path = Path.arc(self.theta1, self.theta2)
+            self._path = Path.arc(theta1, theta2)
             return Patch.draw(self, renderer)
 
         def iter_circle_intersect_on_line(x0, y0, x1, y1):
@@ -1670,8 +1678,6 @@ def iter_circle_intersect_on_line_seg(x0, y0, x1, y1):
             self.get_transform().inverted()
         box_path = box_path.transformed(box_path_transform)
 
-        theta1 = self.theta1
-        theta2 = self.theta2
         thetas = set()
         # For each of the point pairs, there is a line segment
         for p0, p1 in zip(box_path.vertices[:-1], box_path.vertices[1:]):

diff --git a/lib/matplotlib/tests/baseline_images/test_axes/arc_angles.png b/lib/matplotlib/tests/baseline_images/test_axes/arc_angles.png
diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
@@ -982,6 +982,32 @@ def test_canonical():
     ax.plot([1, 2, 3])
 
 
+@image_comparison(baseline_images=['arc_angles'], remove_text=True,
+                  style='default', extensions=['png'])
+def test_arc_angles():
+    from matplotlib import patches
+    # Ellipse parameters
+    w = 2
+    h = 1
+    centre = (0.2, 0.5)
+
+    fig, axs = plt.subplots(3, 3)
+    for i, ax in enumerate(axs.flat):
+        theta2 = i * 360 / 9
+        theta1 = theta2 - 45
+        ax.add_patch(patches.Ellipse(centre, w, h, alpha=0.3))
+        ax.add_patch(patches.Arc(centre, w, h, theta1=theta1, theta2=theta2))
+        # Straight lines intersecting start and end of arc
+        ax.plot([2 * np.cos(np.deg2rad(theta1)) + centre[0],
+                 centre[0],
+                 2 * np.cos(np.deg2rad(theta2)) + centre[0]],
+                [2 * np.sin(np.deg2rad(theta1)) + centre[1],
+                 centre[1],
+                 2 * np.sin(np.deg2rad(theta2)) + centre[1]])
+        ax.set_xlim(-2, 2)
+        ax.set_ylim(-2, 2)
+
+
 @image_comparison(baseline_images=['arc_ellipse'],
                   remove_text=True)
 def test_arc_ellipse():
@@ -990,23 +1016,23 @@ def test_arc_ellipse():
     width, height = 1e-1, 3e-1
     angle = -30
 
-    theta = np.arange(0.0, 360.0, 1.0)*np.pi/180.0
-    x = width/2. * np.cos(theta)
-    y = height/2. * np.sin(theta)
+    theta = np.arange(0.0, 360.0, 1.0) * np.pi / 180.0
+    x = width / 2. * np.cos(theta)
+    y = height / 2. * np.sin(theta)
 
-    rtheta = angle*np.pi/180.
+    rtheta = angle * np.pi / 180.
     R = np.array([
-        [np.cos(rtheta),  -np.sin(rtheta)],
-        [np.sin(rtheta), np.cos(rtheta)],
-        ])
+        [np.cos(rtheta), -np.sin(rtheta)],
+        [np.sin(rtheta), np.cos(rtheta)]])
 
     x, y = np.dot(R, np.array([x, y]))
     x += xcenter
     y += ycenter
 
     fig = plt.figure()
     ax = fig.add_subplot(211, aspect='auto')
-    ax.fill(x, y, alpha=0.2, facecolor='yellow', edgecolor='yellow', linewidth=1, zorder=1)
+    ax.fill(x, y, alpha=0.2, facecolor='yellow', edgecolor='yellow',
+            linewidth=1, zorder=1)
 
     e1 = patches.Arc((xcenter, ycenter), width, height,
                      angle=angle, linewidth=2, fill=False, zorder=2)