An angle is the union of two nonparallel rays originating from the same point; this point is known as the vertex. The rays are known as sides of the angle.
If ray AB is on top of ray BC, then the angle ABC is a zero angle. One complete revolution of a ray gives an angle of 360°.
Depending on the rotation of a ray, an angle can be classified as right, straight, acute, obtuse, or reflex. These angles are defined as follows:
Angle with a ray separated by 90°.
Angle with a ray separated by 180° to form a straight line.
angle with a ray separated by less than 90°.
angle with a ray rotated greater than 90° but less than 180°.
Angle with a ray rotated greater than 180°.
If angles are next to each other, they are called adjacent angles.
If the sum of two angles equals 90°, they are called complimentary angles. For example, 27° and 63° are complimentary angles.
If the sum of two angles equals 180°, they are called supplementary angles. For example, 73°and 107° are supplementary angles.
The important information in this chapter is summarized below.
Straight lines are parallel when they are in the same plane and do not intersect.
A straight angle is 180°.
An acute angle is less than 90°.
A right angle is 90°.
An obtuse angle is greater than 90° but less than 180°.
If the sum of two angles equals 90°, they are complimentary angles.
If the sum of two angles equals 180°, they are supplementary angles.