Two angles are supplementary supplementary if the sum of their measures is 180 degrees .180°. if the measure of an angle is 9 x9x degrees, represent the measure of its supplement supplement as an algebraic expression in x.

The answer is

Step-by-step explanation:

Two angles are supplementary if the sum of their measures is 180°. That means that two angles, let's say, α, and its supplement, β, are supplementary if the following is true:

Now, let's say that α measures 9x degrees, and let us replace in the above expression:

If we now want to represent the measure of the supplementary angle, β, we have to subtract 9x from both sides of the expression to get the final algebraic expression of β in x:

Note that an algebraic expression is just a mathematical relationship between numbers and variables! The goal was to isolate the supplementary angle, β, and find its relationship with the variable x.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

answer: two angles are called supplementary if they add up to 180°. example: the two angles (140° and 40°) are supplementary because they add up to 180°.

step-by-step explanation: