In 2001, Richard Hartley et al. [Visual navigation in a plane using the conformal pint] described a novel entity known as the conformal point P which enables direct measurement of angles in the image. In spite of its convenience, P is plane-dependent. If the angle lies on another plane, the vanishing line changes and hence, the conformal point moves too. Sometimes the angle lies on a virtual plane where the vanishing line is not easy to discover. This paper proposes a novel algorithm to address this problem. After ideal plane stabilization, the angle is marked in both images. Through mapping the angle lines from one image to the target image, the location of the vanishing line in the target image can be determined. With the camera calibrated, the conformal point can be directly determined. The angle can then be computed as in [Visual navigation in a plane using the conformal pint]. Real experiments show that an angle in the 3D world can be computed quite accurately using the proposed method.