Angles in the Plane

Below is a summary of the basic facts about the angles formed in a plane by lines, line segments, and rays.

• Vertical angles and supplementary angles. Two opposite angles formed by two intersecting lines are called vertical angles.

Vertical angles have the same measure.  In the figure above, y = 115° and x = 65°.

Note that any pair of angles next to each other in the figure have measures that add up to 180°. (This is the measure of a straight angle: the angle formed by a straight line.) Two angles whose measures have a sum of 180° are called supplementary angles.

• Parallel lines. When a line intersects a pair of parallel lines, the eight angles formed are related in several ways.
  

The measures of corresponding angles are equal; for example, a and e are equal, as are d and h. Also, several pairs of angles each add up to a straight angle; for example, d + f = 180° and a + g = 180°. Finally, alternate interior angles have equal measures; in the figure, c and f are equal, as are d and e.

• Right angles: A right angle is an angle with a measure of 90°.   
• Perpendicular lines: If two lines intersect and one of the four angles formed is a right angle, the lines are perpendicular.  In this case, all four angles that are formed are right angles.
• Complementary angles: Two angles whose measures have a sum of 90° are called complementary angles.