Welcome! Today we'll explore different types of angles. Angles are geometric figures formed by two rays sharing a common endpoint. They are classified primarily by their measure in degrees. Let's start by examining how angles change as we increase their measure.
Let's examine acute and right angles in detail. An acute angle measures less than 90 degrees and appears sharp and pointed. Common examples include 30, 45, and 60 degrees. A right angle measures exactly 90 degrees and forms a perfect square corner. Right angles are fundamental in geometry and appear everywhere in architecture and design.
Now let's explore obtuse and straight angles. An obtuse angle measures more than 90 degrees but less than 180 degrees. These angles appear wide and open, like 120 or 150 degrees. A straight angle measures exactly 180 degrees and forms a perfectly straight line. When you see a straight angle, the two rays point in completely opposite directions.
Finally, let's examine reflex and full angles. A reflex angle measures more than 180 degrees but less than 360 degrees. These angles represent more than half a rotation, like 270 degrees. A full angle measures exactly 360 degrees and represents a complete rotation. When you make a full turn, you've rotated through a full angle.
Let's explore important angle relationships. Complementary angles are two angles whose measures add up to 90 degrees, like 60 and 30 degrees. Supplementary angles are two angles whose measures add up to 180 degrees, such as 120 and 60 degrees. Vertical angles are opposite angles formed when two lines intersect, and they are always equal in measure. These relationships are fundamental in geometry and help us solve many angle problems.