Angle Addition Postulate

Help and definitions


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First some definitions.


A linear pair is a pair of adjacent angles that are supplementary (which means together they form a straight line).
A vertical pair is formed when two lines cross.  They are sometimes called opposite angles.  They are always congruent to one another.

Example:

Angle 1 and angle 2 are vertical angles. Angle 1 measures 14x + 17 and angle 2 measures 10x + 41. Find x and the measure of angle 1.

Since these are equal to one another:

14x + 17 = 10x + 41

-10x          -10x

4x + 17 = 41

      -17    -17

4x = 24

x = 6

Angle 1 = 14(6) + 17 = 101

CHECK!

Did Angle 2 come out the same?

Angle 2 = 10(6) + 41 = 101