3.2.1 Basic angle Properties
Here are some basic angle properties:
Degree measure:
Angles are measured in degrees. A complete revolution is \( 360 \) degrees.
Types of angles:
Angles can be classified according to their measure.
An acute angle measures less than \( 90 \) degrees, a right-angle measures exactly \( 90 \) degrees, an obtuse angle measures between \( 90 \) and \( 180 \) degrees, and a straight angle measures exactly \( 180 \) degrees.
Complementary angles:
Two angles are complementary if their measures add up to \( 90 \) degrees.
For example, an angle of \( 30 \) degrees and an angle of \( 60 \) degrees are complementary.
Supplementary angles:
Two angles are supplementary if their measures add up to \( 180 \) degrees.
For example, an angle of \( 120 \) degrees and an angle of \( 60 \) degrees are supplementary.
Vertical angles:
Vertical angles are formed when two lines intersect.
The angles opposite each other are called vertical angles, and they have the same measure.
For example, in the diagram below, angles \( 1 \) and \( 3 \) are vertical angles, and angles \( 2 \) and \( 4 \) are vertical angles.
Corresponding angles:
Corresponding angles are formed when a transversal intersects two parallel lines.
Corresponding angles are congruent (have the same measure).
For example, in the diagram below, angles \( 1 \) and \( 5 \), angles \( 2 \) and \( 6 \), angles \( 3 \) and \( 7 \) and angles \( 4 \) and \( 8 \) are corresponding angles.
Alternate interior angles:
Alternate interior angles are formed when a transversal intersects two parallel lines.
Alternate interior angles are congruent (have the same measure).
For example, in the diagram below, angles \( 1 \) and \( 3 \) are alternate interior angles, and angles \( 2 \) and \( 4 \) are alternate interior angles.
