Angles in the Plane

**Angles in the Plane**

In order to work through some of the math questions, you will need to know 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**.