Angles

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:

Right Angle

Angle with a ray separated by 90°.

Straight Angle

Angle with a ray separated by 180° to form a straight line.

Acute Angle 

angle with a ray separated by less than 90°.

Obtuse Angle 

angle with a ray rotated greater than 90° but less than 180°.

Reflex Angle 

Angle with a ray rotated greater than 180°.

Adjacent Angle

If angles are next to each other, they are called adjacent angles.

Complimentary Angles

If the sum of two angles equals 90°, they are called complimentary angles. For example, 27° and 63° are complimentary angles.

Supplementary Angles

If the sum of two angles equals 180°, they are called supplementary angles. For example, 73°and 107° are supplementary angles.

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.