Just like complementaryangles,supplementaryanglesneednot be congruent,or eventouching.Their
definingqualityis that whentheir measuresare addedtogether, the sum is 180º.You can use this information
just as you did with complementaryanglesto solvedifferenttypesof problems.
Example 3
The two anglesbeloware supplementary. If, whatis
?
This processis very straightforward.Sinceyou knowthat the two anglesmustsum to 180º,you can create
an equation.Use a variablefor the unknownanglemeasureand then solvefor the variable.In this case,
let’s call.
So, the measureof and thus.Example 4
Whatis the measureof two congruent,supplementaryangles?Thereis no diagramto help you visualizethis scenario,so you’llhaveto imaginethe angles(or evenbetter,
drawit yourselfby translatingthe wordsinto a picture!).Two supplementaryanglesmustsum to 180º.
Congruentanglesmusthavethe samemeasure.So, you needto find two congruentanglesthat are supple-
mentary. You can divide180º by two to find the valueof eachangle.
Eachcongruent,supplementaryanglewill measure90º. In otherwords,they will be right angles.LinearPairs
Beforewe talk abouta specialpair of anglescalledlinearpairs, we needto defineadjacentangles.Two
anglesare adjacentif they sharethe samevertexand one side,but they do not overlap.In the diagram
below, and are adjacent.