Angle - Geometric Characteristics Of Angles

An angle is typically classified into four categories including acute, right, obtuse, and straight. An acute angle is one which has a degree measurement greater than 0° but less than 90°. A right angle has a 90° angle measurement. An obtuse angle has a measurement greater than 90° but less than 180°, and a straight angle, which looks like a straight line, has a 180° angle measurement.

Two angles are known as congruent angles if they have the same measurement. If their sum is 90°, then they are said to be complementary angles. If their sum is 180°, they are supplementary angles. Angles can be bisected (divided in half) or trisected (divided in thirds) by rays protruding from the vertex.

When two lines intersect, they form four angles. The angles directly across from each other are known as vertical angles and are congruent. The neighboring angles are called adjacent because they share a common side. If the lines intersect such that each angle measures 90°, the lines are then considered perpendicular or orthogonal.

In addition to size, angles also have trigonometric values associated with them such as sine, cosine, and tangent. These values relate the size of an angle to a given length of its sides. These values are particularly important in areas such as navigation, astronomy, and architecture.