When two straight lines meet at a point, they form an angle. The point is called the vertex of the angle, and the lines are called the sides of the angle.

Types of Angles

  1. An acute angle has measure of less than 90 degrees.
  2. A right angle has measure of 90 degrees.
  3. An obtuse angle has measure of greater than 90 degrees.
  4. A straight angle has measure of 180 degrees.

Complementary Angles

Two angles that add together to total 90 degrees. Together, they form a right angle.

Supplementary Angles

Two angles that add together to total 180 degrees. They form a straight angle.

Rules for Lines and Angles

Intersecting Lines

When two lines intersect, the opposite angles (across from each other) are always congruent or equal, and the adjacent angles are always supplementary. Opposite angles are also known as vertical angles. Adjacent angles have a common side, so they are right next to each other.

In the figure, ∠ABC and ∠DBE are congruent, ∠ABC and ∠CBD form a straight line and are, therefore, supplementary.

Parallel Lines intersected by a Transversal

When parallel lines are crossed by a third line that’s not perpendicular to them (called a transversal), the resulting small and large angles share certain properties. Each of the small angles is equal; the large angles are also equal to each other. The measurement of any small angle added to that of any large angle equals 180°.