### Angle - Wikipedia

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However, the two other lines do not have to be parallel in order for a transversal to cross them, as you can see here: A straight angle, also called a flat angle, is formed by a straight line. The measure of this angle is degrees. A straight angle can also be formed by two or more angles that sum to degrees.

### Corresponding Angles: Definition, Theorem & Examples - Video & Lesson Transcript | n3ws.info

Parallel lines are two lines on a two-dimensional plane that never meet or cross. When a transversal passes through parallel lines, there are special properties about the angles that are formed that do not occur when the lines are not parallel.

Notice the arrows on lines m and n towards the left. These arrows indicate that lines m and n are parallel.

## Corresponding Angles: Definition, Theorem & Examples

Corresponding angles are formed when a transversal passes through two lines. The angles that are formed in the same position, in terms of the transversal, are corresponding angles. They are both above the parallel lines and to the right of the transversal. If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

A theorem is a proven statement or an accepted idea that has been shown to be true. The converse of this theorem, which is basically the opposite, is also a proven statement: If two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel. A mixed format with decimal fractions is also sometimes used, e. A nautical mile was historically defined as a minute of arc along a great circle of the Earth. In a two-dimensional Cartesian coordinate systeman angle is typically defined by its two sides, with its vertex at the origin.

The initial side is on the positive x-axiswhile the other side or terminal side is defined by the measure from the initial side in radians, degrees, or turns. With positive angles representing rotations toward the positive y-axis and negative angles representing rotations toward the negative y-axis. When Cartesian coordinates are represented by standard position, defined by the x-axis rightward and the y-axis upward, positive rotations are anticlockwise and negative rotations are clockwise.

In three-dimensional geometry, "clockwise" and "anticlockwise" have no absolute meaning, so the direction of positive and negative angles must be defined relative to some reference, which is typically a vector passing through the angle's vertex and perpendicular to the plane in which the rays of the angle lie. In navigationbearings or azimuth are measured relative to north.

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Alternative ways of measuring the size of an angle[ edit ] There are several alternatives to measuring the size of an angle by the angle of rotation. The grade of a slopeor gradient is equal to the tangent of the angle, or sometimes rarely the sine.

## Geometry help! Alternate interior/exterior angles.?

A gradient is often expressed as a percentage. In rational geometry the spread between two lines is defined as the square of the sine of the angle between the lines. As the sine of an angle and the sine of its supplementary angle are the same, any angle of rotation that maps one of the lines into the other leads to the same value for the spread between the lines.