diff --git a/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h b/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h
index f4ec5137e55..ae5ba565f61 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h
@@ -40,13 +40,28 @@ namespace CartesianKernelFunctors {
   template <typename K>
   class Angle_2
   {
-    typedef typename K::Point_2 Point_2;
+    typedef typename K::Point_2  Point_2;
+    typedef typename K::Vector_2 Vector_2;
   public:
     typedef typename K::Angle   result_type;
 
+    result_type
+    operator()(const Vector_2& u, const Vector_2& v) const
+    { return angleC2(u.x(), u.y(), v.x(), v.y()); }
+
     result_type
     operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
     { return angleC2(p.x(), p.y(), q.x(), q.y(), r.x(), r.y()); }
+
+    result_type
+    operator()(const Point_2& p, const Point_2& q, 
+               const Point_2& r, const Point_2& s) const
+    {
+      return angleC2(p.x(), p.y(),
+		     q.x(), q.y(),
+		     r.x(), r.y(),
+                     s.x(), s.y());
+    }
   };
 
   template <typename K>
diff --git a/Cartesian_kernel/include/CGAL/predicates/kernel_ftC2.h b/Cartesian_kernel/include/CGAL/predicates/kernel_ftC2.h
index b818a745c92..67ef5102bdd 100644
--- a/Cartesian_kernel/include/CGAL/predicates/kernel_ftC2.h
+++ b/Cartesian_kernel/include/CGAL/predicates/kernel_ftC2.h
@@ -420,6 +420,15 @@ orientationC2(const FT &ux, const FT &uy, const FT &vx, const FT &vy)
   return sign_of_determinant(ux, uy, vx, vy);
 }
 
+template < class FT >
+inline
+typename Same_uncertainty_nt<Angle, FT>::type
+angleC2(const FT &ux, const FT &uy,
+        const FT &vx, const FT &vy)
+{
+  return enum_cast<Angle>(CGAL_NTS sign(ux*vx + uy*vy));
+}
+
 template < class FT >
 inline
 typename Same_uncertainty_nt<Angle, FT>::type
@@ -430,6 +439,17 @@ angleC2(const FT &px, const FT &py,
   return enum_cast<Angle>(CGAL_NTS sign((px-qx)*(rx-qx)+(py-qy)*(ry-qy)));
 }
 
+template < class FT >
+inline
+typename Same_uncertainty_nt<Angle, FT>::type
+angleC2(const FT &px, const FT &py,
+        const FT &qx, const FT &qy,
+        const FT &rx, const FT &ry,
+        const FT &sx, const FT &sy)
+{
+  return enum_cast<Angle>(CGAL_NTS sign((px-qx)*(rx-sx)+(py-qy)*(ry-sy)));
+}
+
 template < class FT >
 CGAL_KERNEL_MEDIUM_INLINE
 typename Equal_to<FT>::result_type
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h b/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
index 89ccb4a9931..8eb1217af51 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
@@ -56,6 +56,7 @@ namespace HomogeneousKernelFunctors {
   class Angle_2
   {
     typedef typename K::Point_2             Point_2;
+    typedef typename K::Vector_2            Vector_2;
     typedef typename K::Construct_vector_2  Construct_vector_2;
     Construct_vector_2 c;
   public:
@@ -66,7 +67,17 @@ namespace HomogeneousKernelFunctors {
 
     result_type
     operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
-    { return enum_cast<Angle>(CGAL_NTS sign(c(q,p) * c(q,r))); }
+    { return operator()(c(q,p), c(q,r)); }
+
+    result_type
+    operator()(const Point_2& p, const Point_2& q, 
+               const Point_2& r, const Point_2& s) const
+    { return operator()(c(q,p), c(s,r)); }
+
+    result_type
+    operator()(const Vector_2& u, const Vector_2& v) const
+    { return enum_cast<Angle>(CGAL_NTS sign(u * v)); }
+
     // FIXME: scalar product
   };
 
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_Angle_2.tex b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_Angle_2.tex
index 5fcf48603fa..98c7186c446 100644
--- a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_Angle_2.tex
+++ b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_Angle_2.tex
@@ -5,15 +5,25 @@ A model for this must provide:
 
 \ccCreationVariable{fo}
 
+\ccMemberFunction{Angle operator()(const Kernel::Vector_2&u, 
+                                   const Kernel::Vector_2&v);}
+{returns \ccStyle{OBTUSE}, \ccStyle{RIGHT} or \ccStyle{ACUTE} depending
+on the angle formed by the two vectors $u$ and $v$.}
+
 \ccMemberFunction{Angle operator()(const Kernel::Point_2&p, 
                                    const Kernel::Point_2&q, 
                                    const Kernel::Point_2&r);}
 {returns \ccStyle{OBTUSE}, \ccStyle{RIGHT} or \ccStyle{ACUTE} depending
 on the angle formed by the three points $p$, $q$, $r$ ($q$ being the vertex of
-the angle).}
+the angle). The returned value is the same as \ccc{operator()(p - q, r - q)}.}
 
-\ccRefines
-\ccc{AdaptableFunctor} (with three arguments)
+\ccMemberFunction{Angle operator()(const Kernel::Point_2&p, 
+                                   const Kernel::Point_2&q, 
+                                   const Kernel::Point_2&r, 
+                                   const Kernel::Point_2&s);}
+{returns \ccStyle{OBTUSE}, \ccStyle{RIGHT} or \ccStyle{ACUTE} depending
+on the angle formed by the two vectors $pq$, $rs$. The returned value is
+the same as \ccc{operator()(q - p, s - r)}.}
 
 \ccSeeAlso
 \ccRefIdfierPage{CGAL::angle}  \\
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/angle.tex b/Kernel_23/doc_tex/Kernel_23_ref/angle.tex
index 6ce1538344a..dbc6dd75016 100644
--- a/Kernel_23/doc_tex/Kernel_23_ref/angle.tex
+++ b/Kernel_23/doc_tex/Kernel_23_ref/angle.tex
@@ -1,13 +1,28 @@
 %\ccHtmlNoRefLinks
 \begin{ccRefFunction}{angle}
 
+\ccHtmlNoLinks
+\ccFunction{Angle angle(const Vector_2<Kernel>&u, 
+                        const Vector_2<Kernel>&v);}
+{returns \ccStyle{OBTUSE}, \ccStyle{RIGHT} or \ccStyle{ACUTE} depending
+on the angle formed by the two vectors $u$ and $v$.}
+
 \ccHtmlNoLinks
 \ccFunction{Angle angle(const Point_2<Kernel>& p,
                         const Point_2<Kernel>& q,
                         const Point_2<Kernel>& r);}
 {returns \ccStyle{OBTUSE}, \ccStyle{RIGHT} or \ccStyle{ACUTE} depending
 on the angle formed by the three points $p$, $q$, $r$ ($q$ being the vertex of
-the angle).}
+the angle). The returned value is the same as \ccc{angle(p - q, r - q)}.}
+
+\ccHtmlNoLinks
+\ccFunction{Angle angle(const Point_2<Kernel>& p,
+                        const Point_2<Kernel>& q,
+                        const Point_2<Kernel>& r,
+                        const Point_2<Kernel>& s);}
+{returns \ccStyle{OBTUSE}, \ccStyle{RIGHT} or \ccStyle{ACUTE} depending
+on the angle formed by the two vectors $pq$, $rs$. The returned value is
+the same as \ccc{angle(q - p, s - r)}.}
 
 \ccHtmlNoLinks
 \ccFunction{Angle angle(const Point_3<Kernel>& p,
diff --git a/Kernel_23/include/CGAL/Kernel/global_functions_2.h b/Kernel_23/include/CGAL/Kernel/global_functions_2.h
index c26beb4f5fc..b96a25e3010 100644
--- a/Kernel_23/include/CGAL/Kernel/global_functions_2.h
+++ b/Kernel_23/include/CGAL/Kernel/global_functions_2.h
@@ -49,6 +49,15 @@ operator!=(const Point_2<K> &p, const Origin& o)
   return p != Point_2<K>(o);
 }
 
+template < class K >
+inline
+Angle
+angle(const Vector_2<K> &u,
+      const Vector_2<K> &v)
+{
+  return internal::angle(u, v, K());
+}
+
 template < class K >
 inline
 Angle
@@ -59,6 +68,17 @@ angle(const Point_2<K> &p,
   return internal::angle(p, q, r, K());
 }
 
+template < class K >
+inline
+Angle
+angle(const Point_2<K> &p,
+      const Point_2<K> &q,
+      const Point_2<K> &r,
+      const Point_2<K> &s)
+{
+  return internal::angle(p, q, r, s, K());
+}
+
 template < class K >
 inline
 typename K::Boolean
diff --git a/Kernel_23/include/CGAL/Kernel/global_functions_internal_2.h b/Kernel_23/include/CGAL/Kernel/global_functions_internal_2.h
index 53eefb23e45..913abd1b4eb 100644
--- a/Kernel_23/include/CGAL/Kernel/global_functions_internal_2.h
+++ b/Kernel_23/include/CGAL/Kernel/global_functions_internal_2.h
@@ -40,6 +40,15 @@ namespace CGAL {
 
 namespace internal {
 
+template < class K >
+inline
+typename K::Angle
+angle(const typename K::Vector_2 &u,
+      const typename K::Vector_2 &v, const K& k)
+{
+  return k.angle_2_object()(u, v);
+}
+
 template < class K >
 inline
 typename K::Angle
@@ -50,6 +59,17 @@ angle(const typename K::Point_2 &p,
   return k.angle_2_object()(p, q, r);
 }
 
+template < class K >
+inline
+typename K::Angle
+angle(const typename K::Point_2 &p,
+      const typename K::Point_2 &q,
+      const typename K::Point_2 &r,
+      const typename K::Point_2 &s, const K& k)
+{
+  return k.angle_2_object()(p, q, r, s);
+}
+
 template < class K >
 inline
 typename K::Boolean
diff --git a/Kernel_23/test/Kernel_23/include/CGAL/_test_angle.h b/Kernel_23/test/Kernel_23/include/CGAL/_test_angle.h
index 2d78befcddb..cbe53f8f78a 100644
--- a/Kernel_23/test/Kernel_23/include/CGAL/_test_angle.h
+++ b/Kernel_23/test/Kernel_23/include/CGAL/_test_angle.h
@@ -32,12 +32,23 @@ _test_angle(const R&)
   typedef CGAL::Point_2<R>  Point_2;
   typedef CGAL::Point_3<R>  Point_3;
 
+  typedef CGAL::Vector_2<R> Vector_2;
+  typedef CGAL::Vector_3<R> Vector_3;
+
   Point_2 p(RT(2),RT(1));
   Point_2 q(RT(5),RT(4));
   Point_2 r(RT(5),RT(10));
+  Point_2 s(RT0, RT0);
+
+  Vector_2 qp = p - q;
+  Vector_2 qr = r - q;
 
   assert( CGAL::angle( p, q, r ) == CGAL::OBTUSE );
+  assert( CGAL::angle( qp , qr ) == CGAL::OBTUSE );
+  assert( CGAL::angle( q, p, q, r ) == CGAL::OBTUSE );
   assert( CGAL::angle( r, p, q ) == CGAL::ACUTE );
+  assert( CGAL::angle( p, s, q , r) == CGAL::OBTUSE );
+  assert( CGAL::angle( p, r, s , q) == CGAL::ACUTE );
 
   Point_2 e0( RT1, RT0);
   Point_2 e1( RT0, RT1);
diff --git a/Kernel_23/test/Kernel_23/include/CGAL/_test_new_2.h b/Kernel_23/test/Kernel_23/include/CGAL/_test_new_2.h
index a189ef0d0e4..6110c53e416 100644
--- a/Kernel_23/test/Kernel_23/include/CGAL/_test_new_2.h
+++ b/Kernel_23/test/Kernel_23/include/CGAL/_test_new_2.h
@@ -611,6 +611,8 @@ test_new_2(const R& rep)
   typename R::Angle_2 angle
         = rep.angle_2_object();
   Angle tmp58 = angle(p2,p3,p4);
+  tmp58 = angle(p1, p2, p3, p4);
+  tmp58 = angle(v2, v3);
 
   use(v1); use(v4); use(r1);
   use(d4); use(d5);