# angle

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## angle,

in mathematics, figure formed by the intersection of two straight lines; the lines are called the sides of the angle and their point of intersection the vertex of the angle. Angles are commonly measured in degrees (°) or in radians. If one side and the vertex of an angle are fixed and the other side is rotated about the vertex, it sweeps out a complete circle of 360° or 2π radians with each complete rotation. Half a rotation from 0° or 0 radians results in a straight angle, equal to 180° or π radians; the sides of a straight angle form a straight line. A quarter rotation (half of a straight angle) results in a right angle, equal to 90° or π/2 radians; the sides of a right angle are perpendicular to one another. An angle less than a right angle is acute, and an angle greater than a right angle is obtuse. Two angles that add up to a right angle are complementary. Two angles that add up to a straight angle are supplementary. One of the geometric problems of antiquitygeometric problems of antiquity,
three famous problems involving elementary geometric constructions with straight edge and compass, conjectured by the ancient Greeks to be impossible but not proved to be so until modern times.
is the trisection of an angle. Angles can also be formed by higher–dimensional figures, as by a line and a plane, or by two intersecting planes.

## Angle (Angular)

(religion, spiritualism, and occult)

The term “angle” can be used in two different ways in astrology. In its primary, traditional meaning, angle refers to one of the four “corners” (figuratively speaking) of a chart—namely, the cusps of the first, fourth, seventh, and tenth houses. Planets making a conjunction with the angles—which are sometimes called angular planets, particularly when they are in an angular house—are said to exercise an especially strong influence over the entire horoscope. In practice, astrologers pay the most attention to angular planets in the first and tenth houses. Angle is also used as an alternative term for aspect, as when one talks about the angular relationship between two planets.

## angle

[′aŋ·gəl]
(mathematics)
The geometric figure, arithmetic quantity, or algebraic signed quantity determined by two rays emanating from a common point or by two planes emanating from a common line.

## angle

1. The figure made by two lines that meet.
2. The difference in direction of such intersecting lines, or the space within them.
3. A projecting or sharp corner.
4. A secluded area resembling a corner; a nook.
5. An L-shaped metal member; an angle iron.
7. A fitting on a gutter for rainwater which changes the gutter’s direction.

## angle

1. the space between two straight lines that diverge from a common point or between two planes that extend from a common line
2. the shape formed by two such lines or planes
3. the extent to which one such line or plane diverges from another, measured in degrees or radians
References in periodicals archive ?
This information is based on the findings of this study as applicable to angle measure.
Spatial reasoning was discussed in the last section on angle measure as students struggled with spatial orientation and spatial visualization.
Angle measure reproducibility between manual and computerized tracing methods did not show significant differences, suggesting that both methods offer equal diagnostic validity.
In the same way, brightness obviously is ignored completely by this angle measure used in Astronomy.
5 some of the systematic errors of vertical angle measures can be noted, though more serious and thorough analysis of results is needed.
From our experience, even though most students are familiar with latitudinal and longitudinal lines and the names of these lines (e.g., latitude 32 degrees south, longitude 128 degrees east), they usually do not realise that the word degree refers to the angle measure, and do not know how to measure it even among the ones with the realisation.
Unmeasured shape makers are replaced by measured shape makers, which display angle measures and side lengths that are instantaneously updated when the shape makers are manipulated.
For example, in explaining why all of the angles measured 135[degrees], one student wrote (refer to Figure 6): "If angle BDQ is 45 degrees, then angle MQP is 45 degrees, because corresponding angles are congruent where parallel lines are present (parallel lines are present because of the square)." Two lines later, the student continued: "Now, a trapezoid DQMF exists (DF is parallel to QM, because it is already established that the angles FDQ and DQM are 45 degrees and 135 degrees respectively, and if the same side interior angles are supplementary, then the lines are parallel)." In the first statement, the student essentially assumes the segments are parallel to determine the angle measures. The student then uses those angle measures to explain why the two segments are parallel.
The effect of malnutrition on phase angle measures was measured in rainbow trout in fresh water by repeatedly measuring the phase angle in fed and fasted juvenile rainbow trout over a period of four weeks starting in December 2004.
Calibration and testing of the geodetic angle measuring instruments has always been a serious problem and if calibration of the horizontal angle measurements could be quite efficiently accomplished using standard precise turn tables (quite widely implemented in metrology and industry), the calibration of vertical angle measures required some special instrumentation.
During fifth grade, Luke and his classmates applied angle-measurement ideas in map contexts in which they estimated, compared, measured, added, and subtracted angle measures. The analysis in the following paragraphs notes the instances when Luke is building on these past mathematical experiences, formulating his own arguments, or engaging in some combination of the two.
In my work with sixth graders, all the students confidently stated that the sum of the angle measures is 180 degrees.

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