在数学中，特别是几何学中，角度由两条射线（或线）形成，这两条射线（或线）从相同的点开始或共享相同的端点。该角度测量两个臂或两个角度之间的转弯量，通常以度或弧度来度量。两条光线相交或相遇的地方称为顶点。角度由其度量（例如，度）定义，并且不取决于角度边的长度。 “angle”这个词来自拉丁语angulus，意思是“角落”。它与希腊词ankylοs有关，意思是“弯曲，弯曲”，英文单词“脚踝”。希腊语和英语单词都来自Proto-Indo-European词根“ank-”，意思是“弯曲”或“弯曲”。正好90度的角度称为直角。小于90度的角度称为锐角。恰好180度的角度称为直角（这显示为直线）。大于90度且小于180度的角度称为钝角。大于直角但小于1转（180度和360度之间）的角度称为反射角。 360度或等于一整圈的角度称为全角度或完整角度。对于钝角的示例，典型的屋顶的角度通常以钝角形成。钝角大于90度，因为水会在屋顶上汇集（如果是90度），或者屋顶没有水向下流动的角度。角度通常使用字母命名，以识别角度的不同部分：顶点和每条射线。例如，角度BAC，标识以“A”作为顶点的角度。它被光线包围，“B”和“C”。有时，为了简化角度的命名，它简称为“角度A”。当两条直线在一点处相交时，形成四个角度，例如“A”，“B”，“C”和“D”角。由形成“X”形状的两条交叉直线形成的彼此相对的一对角度被称为垂直角度或相反角度。相反的角度是彼此的镜像。角度将是相同的。这些对被命名为第一。由于这些角度具有相同的度数度量，因此这些角度被认为是相等或一致的。例如，假装字母“X”是这四个角度的一个例子。 “X”的顶部形成“v”形，称为“角度A”。该角度与X的底部完全相同，形成“^”形状，称为“角度B”。同样，“X”的两边形成“>”和“<”形状。那些将是角度“C”和“D”。 C和D都具有相同的角度，它们是相反的角度并且是一致的。在该相同的示例中，“角度A”和“角度C”彼此相邻，它们共用一个臂或侧面。此外，在该示例中，角度是补充的，这意味着组合的两个角度中的每一个等于180度（相交的那些直线中的一条形成四个角度）。 “角度A”和“角度D”也是如此。

美国杜克大学数学Assignment代写:角度的定义

In mathematics, particularly geometry, angles are formed by two rays (or lines) that begin at the same point or share the same endpoint. The angle measures the amount of turn between the two arms or sides of an angle and is usually measured in degrees or radians. Where the two rays intersect or meet is called the vertex. An angle is defined by its measure (for example, degrees) and is not dependent upon the lengths of the sides of the angle. The word “angle” comes from the Latin word angulus, meaning “corner.” It is related to the Greek word ankylοs meaning “crooked, curved,” and the English word “ankle.” Both Greek and English words come from the Proto-Indo-European root word “ank-” meaning “to bend” or “bow.” Angles that are exactly 90 degrees are called right angles. Angles less than 90 degrees are called acute angles. An angle that is exactly 180 degrees is called a straight angle (this appears as a straight line). Angles that are greater than 90 degrees and less than 180 degrees are called obtuse angles. Angles that are larger than a straight angle but less than 1 turn (between 180 degrees and 360 degrees) are called reflex angles. An angle that is 360 degrees, or equal to one full turn, is called a full angle or complete angle. For an example of an obtuse angle, the angle of a typical house rooftop is often formed at an obtuse angle. An obtuse angle is greater than 90 degrees since water would pool on the roof (if it was 90 degrees) or if the roof did not have a downward angle for water to flow. Angles are usually named using alphabet letters to identify the different parts of the angle: the vertex and each of the rays. For example, angle BAC, identifies an angle with “A” as the vertex. It is enclosed by the rays, “B” and “C.” Sometimes, to simplify the naming of the angle, it is simply called “angle A.” When two straight lines intersect at a point, four angles are formed, for example, “A,” “B,” “C,” and “D” angles. A pair of angles opposite each other, formed by two intersecting straight lines that form an “X”-like shape, are called vertical angles or opposite angles. The opposite angles are mirror images of each other. The degree of angles will be the same. Those pairs are named first. Since those angles have the same measure of degrees, those angles are considered equal or congruent. For example, pretend that the letter “X” is an example of those four angles. The top part of the “X” forms a “v” shape, that would be named “angle A.” The degree of that angle is exactly the same as the bottom part of the X, which forms a “^” shape, and that would be called “angle B.” Likewise, the two sides of the “X” form a “>” and an “<” shape. Those would be angles “C” and “D.” Both C and D would share the same degrees, they are opposite angles and are congruent. In this same example, “angle A” and “angle C” and are adjacent to each other, they share an arm or side. Also, in this example, the angles are supplementary, which mean that each of the two angles combined equals 180 degrees (one of those straight lines that intersected to form the four angles). The same can be said of “angle A” and “angle D.”