Angle, in plane geometry, is a figure formed by two rays with the same end point. A ray is a part of a line extending indefinitely in one direction from a point. The point where the rays of an angle meet is called the vertex, and the rays themselves are known as the sides.
The size of an angle is usually measured in degrees. When the rays make a square corner, the angle is a right angle. A right angle has 90 degrees (90°). An acute angle has less than 90°. An obtuse angle has between 90° and 180°. An angle of 180° is a straight angle because its sides form a straight line. Two angles are complementary if their sum is 90°. They are supplementary if their sum is 180°. People use a simple device called a protractor to measure angles. Angles can also be measured in units called radians (see Radian ).
In trigonometry, an angle is considered to consist of a fixed, or initial, side and a rotating, or terminal, side. The amount and direction of rotation of the terminal side determine the size of the angle and whether it is positive or negative. Positive angles are formed when the rotation of the terminal side is counterclockwise. Negative angles are formed when the rotation is clockwise. If one hand of a clock is fixed at 3 and the other hand starts at 3 and turns counterclockwise until it reaches 12, an angle of 90° results. This rotation is known as a quarter turn. A half turn results in an angle of 180°; a three-quarter turn, in an angle of 270°; and a full turn, in an angle of 360°. A second complete rotation of the terminal side generates angles between 360° and 720°, a third rotation produces angles between 720° and 1,080°, and so forth for all positive angles.
Negative angles are formed when the terminal side moves clockwise. Compass directions in naval navigation are given by means of angles measured in the clockwise direction from 12. But the measurements are given in positive numbers.
