###### Answer: has two rays that share a common endpoint

The size of a geometric angle is usually characterized by the magnitude of the smallest rotation that maps one of the rays into the other. Angles that have the same size are said to be equal or congruent or equal in measure. In some contexts such as identifying a point on a circle or describing the orientation of an object in two dimensions relative to a reference orientation angles that differ by an exact multiple of a full turn are effectively equivalent. In other contexts such as identifying a point on a spiral

The size of a geometric angle is usually characterized by the magnitude of the smallest rotation that maps one of the rays into the other. Angles that have the same size are said to be equal or congruent or equal in measure. In some contexts such as identifying a point on a circle or describing the orientation of an object in two dimensions relative to a reference orientation angles that differ by an exact multiple of a full turn are effectively equivalent. In other contexts such as identifying a point on a spiral curve or describing the cumulative rotation of an object in two dimensions relative to a reference orientation angles that differ by a non-zero multiple of a full turn are not equivalent. In order to measure an angle θ a circular arc centered at the vertex of the angle is drawn e.g. with a pair of compasses. The ratio of the length s of the arc by the radius r of the circle is the measure of the angle in radians. The measure of the angle in another angular unit is then obtained by multiplying its measure in radians by the scaling factor k/2π where k is the measure of a complete turn in the chosen unit (for example 360 for degrees or 400 for gradians): ${\displaystyle \theta =k{\frac {s}{2\pi r}}.}$ The value of θ thus defined is independent of the size of the circle: if the length of the radius is changed then the arc length changes in the same proportion so the ratio s/r is unaltered. (Proof. The formula above can be rewritten as k = θr/s. One turn for which θ = n units corresponds to an arc equal in length to the circle’s circumference which is 2πr so s = 2πr. Substituting n for θ and 2πr for s in the formula results in k = nr/2πr = n/2π.)

By examining the unit circle one can establish the following properties of the trigonometric functions. Reflections . When the direction of a Euclidean vector is represented by an angle this is the angle determined by the free vector (starting at the origin) and the positive x-unit vector.

In geometry and trigonometry a right angle is an angle of exactly 90° (degrees) corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal then they are right angles. The term is a calque of Latin angulus rectus; here rectus means “upright” referring to the vertical per…