# Angle Definitions for Land Surveyors

**angle—**The difference in direction between two convergent lines. Classed as horizontal, vertical, oblique, spherical, or ellipsoidal, depending on whether it is measured in a horizontal, vertical, or inclined plane, or in a curved surface.

**angle, acute—**An angle less than a right angle (90° or π/2 radians). See also *angle, complement of*

**angle, adjusted—**An adjusted value of an angle. An adjusted angle may be derived either from an observed angle or from a concluded angle.

**angle, azimuth—**The direction of one point or object, with respect to another, where the direction of the line is expressed as the clockwise angle from 0° to 360°, from the reference meridian. The azimuth angle is measured from South in geodesy, and from North in navigation. Either is acceptable in cadastral surveys. Quadrantal azimuths are properly called bearings; half circle azimuths are used in astronomy. The reference meridian can be assumed, grid, magnetic, astronomic, or geodetic. See also *angle, zenith.*

**angle, central**–^{1} The angle at the center of radius of a circular arc included between the radii which pass through beginning (P.C.) and end (PT) of the arc. This angle is equal to the change in direction of the tangents to the arc which pass through the P.C. and P.T. In alinement surveys it is commonly called the delta (△) angle. ^{2} The angle, in curve systems containing compound curves, or spiral and circular curves, between the beginning and ending radius, or the beginning and ending tangents. For spirals the central angle is called theta (θ), or △_{s}. See also *angle, theta.*

**angle, complement of—**The difference between an acute angle and one right angle (90° or π/2 radians). See also *angle, acute.*

**angle, concluded—**An interior angle between adjacent sides of a closed figure obtained by subtracting the sum of all the other interior angles of the figure from the theoretical value of the sum of all interior angles.

**angle, deflection—**A horizontal angle measured from the prolongation of the preceding line, right or left, to the following line.

**angle, delta—**See *angle, central.*

**angle, depression—**The vertical angle measured at the perspective center between the true horizon and the photograph perpendicular.

**angle, dihedral—**The angle formed by two intersecting planes. The dihedral angle is measured in the plane which is perpendicular to each of the two intersecting planes and to the line of their intersection.

**angle, dip**–^{1} In topographic surveying, the vertical angle of the observation point between the plane of the true horizon and a sight line to the apparent horizon. ^{2} In photogrammetry, the vertical angle, at the air station, between the true and the apparent horizon, which is due to flight height, Earth curvature, and refraction.

**angle, direct—**An angle measured directly between two lines, as distinguished in transit traverse from a deflection angle. See also *angle to right, angle to left.*

**angle, distance—**The two angles in a triangle opposite the known side and the side being computed when using the law of sines.

**angle, explement of—**The difference between an angle and four right’ angles (360° or 2π radians).

**angle, exterior**—The angle between any two adjacent sides on the exterior of a triangle or polygon.

**angle, horizontal—**An angle in a horizontal plane. The directions may be to objects in the horizontal plane; or they may be the lines of intersection of the horizontal plane with the vertical planes containing the objects.

**angle**, **included**—The interior angle between adjacent sides in a triangle or polygon.

**angle, interior-**1 An angle formed between two sides within a triangle or polygon. 2 For alignment and/or boundary descriptions, the interior angle is 180 degrees minus the central angle, if the angle is equal to or less than 180 degrees; otherwise, it is the central angle minus 180 degrees.

**angle, measured—**An angle measured using an instrument without any application of corrections for local conditions.

**angle, obtuse—**An angle greater than one right angle (90° or π radians), and less than two right angles (180° or π radians).

**angle, right—**The angle bounded by two radii that intercept a quarter of a circle. An angle of 90 degrees on the sexagesimal system. An angle of 100 grads on the centesimal system.

**angle, skew—**The acute angle formed between a line normal to one center line and another center line. The angle that two intersecting lines deviate from a right angle (90° or π/2 radians).

**angle, spherical—**An angle between great circles on a sphere. A spherical angle is measured either by the dihedral angle of the planes of great circles; or by the plane angle between tangents to great circles at their intersection.

**angle, spheroidal—**An angle between two curves on an ellipsoid, measured by the angle between their tangents at the point of intersection.

**angle, straight—**Two right angles (180° or π** **radians).

**angle,** **supplement of—**The difference between an angle and two right angles (180° or π** **radians).

**angle, theta—**^{1} In Lambert’s Conformal Conic Projection, the angle of convergence, on the developed surface of the cone, between the central meridian and the meridian through the point. ^{2} In Euler Spiral (clothoid), the central angle of the spiral measured at the point of intersection of the tangents passing through the T.S. and the S.T points of the spiral. Also known as the theta (θ) or △_{s} angle. See also *angle, central.*

**angle, vertical—**An angle in a vertical plane. In surveying, one of the directions which forms a vertical angle is usually either the direction of the vertical (zenith), in which case the angle is called the “zenith distance;” or the line of intersection of the vertical plane in which the angle lies with the plane of the horizon, in which case the angle is called the “angle of elevation” or “angle of depression,” or simply the “altitude.”

**angle, zenith—**The angle less than 180° between the plane of the celestial meridian and the vertical plane containing the observed object, reckoned from the direction of the elevated pole. The spherical angle at the zenith in the astronomic triangle which is composed of the pole, the zenith, and the celestial body. See also *angle, azimuth.*

**angle equation**—See *equation, angle.*

**angle method of adjustment**—See *adjustment, angle method. *angle of convergence—See *parallax.*

**angle of coverage**—The apex angle of the cone of rays passing through the front nodal point of a lens; angle of filed. See also *lens, narrow-angle; lens, **normal-angle; wide-angle lens.*

**angle of current**—The angular difference between 90° and the angle made by the current with a measuring section.

**angle of field**—See *angle of coverage.*

**angle of inclination**—An angle of elevation or an angle of depression. See also *altitude.*

**angle point**–^{1} A monument marking a point, on an irregular boundary line, reservation line, boundary of a private claim, or a re-established, non-riparian meander line, at which a change in direction occurs. ^{2} A marker at a point on a traverse, to indicate a change in direction of the traverse at that point. ^{3} A point, in a survey, at which the alignment or boundary changes direction from its previous course. ^{4} A marker placed to indicate a point at which there is a change in the direction of a surveyed line.

**angle to left**—The horizontal angle measured counter-clockwise from the preceding line to the following one. See also *angle, direct.*

**angle to right**—The horizontal angle measured clockwise from the preceding line to the following one. See also *angle, direct.*

**angular distortion**—See *distortion, angular; conformality. *

**angular elevation**—See *altitude.*

**angular error of closure**—See *error of closure *(definition 2).

**angular magnification**—See *magnification, angular *[OPTICS].

**angular parallax**—See *parallax.*

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Source: NSPS “Definitions of Surveying and Related Terms“, used with permission.

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