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. The size of an angle depends on how much one side rotates away from the other side. An angle is usually measured in degrees or radians.

Types of Angles

  1. An acute angle has measure of less than 90 degrees. Like an acute, or sharp, the acute angle has a sharp point.

  2. A right or perpendicular angle has measure of 90 degrees. It makes up a square corner.

  3. An obtuse angle has measure of greater than 90 degrees but less than 180 degrees. The opposite of an acute angle, an obtuse angle is dull rather than sharp.

  4. A straight angle has measure of 180 degrees. A straight angle appears to be a straight line or line segment.

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.

Similar: Objects that have the same shape but may have different sizes.

Congruent: Objects that are equal in size and shape. Two line segments with the same length, two angles with the same measure, and two triangles with corresponding sides of equal lengths and angles that have equal degree measures are congruent.

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°.