Here is the English translation of your Chinese article on "Angle":

Angle

In geometry, an angle is a figure formed by two rays or lines that share a common endpoint. This common point is called the vertex of the angle, and the two rays are called the sides or arms of the angle.

Angles are measured in degrees, radians, or other units of angular measure. In everyday language, we often use terms like "acute," "obtuse," or "right" to describe angles based on their size: an acute angle is less than 90°, an obtuse angle is between 90° and 180°, and a right angle is exactly 90°.

When two lines intersect, they form vertical opposite angles that are equal in measure. For example, if one angle measures 30°, the vertically opposite angle will also measure 30°.

The concept of an angle extends beyond geometry into fields like trigonometry, physics, and engineering, where understanding angular relationships is crucial for problem-solving.

This translation captures the essence of "Angle" while ensuring proper technical terms are used. Let me know if you'd like further refinements!