SOLUTION: In trapezoid ABCD (not shown), m∠A = x/2+ 30, m∠B = x/3+ 50, and m∠C = x/5+ 50. Find all possible values of x. (Enter your answers as a comma-separated list.)

Algebra ->  Formulas -> SOLUTION: In trapezoid ABCD (not shown), m∠A = x/2+ 30, m∠B = x/3+ 50, and m∠C = x/5+ 50. Find all possible values of x. (Enter your answers as a comma-separated list.)      Log On


   

Question 1193156: In trapezoid ABCD (not shown),
m∠A =
x/2+ 30, m∠B =
x/3+ 50, and m∠C =
x/5+ 50.
Find all possible values of x. (Enter your answers as a comma-separated list.)
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!



∠B and ∠C are supplementary because they are interior angles on 
the same side of transversal BC which cuts parallel lines 
AB and CD.  Therefore: 

m∠B + m∠C = 180o

%28x%2F3%2B50%5Eo%29%2B%28x%2F5%2B50%5Eo%29=180%5Eo
x%2F3%2B50%5Eo%2Bx%2F5%2B50%5Eo=180%5Eo
x%2F3%2Bx%2F5%2B100%5Eo=180%5Eo
x%2F3%2Bx%2F5=80%5Eo
Multiply through by 15

Solve for x. 
That's a linear equation, so there will be only one value.

Edwin

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The response from the other tutor is not complete; there are two different trapezoids that are possible with the given information. That fact is suggested by the instructions that say to find "all possible values" of x.

Case 1: angles A and B are supplementary

%28x%2F2%2B30%29%2B%28x%2F3%2B50%29=180
x%2F2%2Bx%2F3=100
%285%2F6%29x=100
x=100%286%2F5%29=120

That value for x leads to A=90, B=90, C=74, D=116

ANSWER 1: one possible value for x is 100

Case 2: angles B and C are supplementary

%28x%2F3%2B50%29%2B%28x%2F5%2B50%29=180
x%2F3%2Bx%2F5=80
%288%2F15%29x=80
x=80%2815%2F8%29=150

That value for x leads to A=105, B=100, C=80, D=75

ANSWER 2: another possible value for x is 150