SOLUTION: if m deg=(5x-4) m gef=(7x-8) m deh=(9y+5) find the values of x and y

Algebra ->  Angles -> SOLUTION: if m deg=(5x-4) m gef=(7x-8) m deh=(9y+5) find the values of x and y       Log On


   

Question 1203467: if m deg=(5x-4) m gef=(7x-8) m deh=(9y+5) find the values of x and y
Found 3 solutions by josgarithmetic, MathLover1, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Your notation is either faulty, or wrong, or ambiguous. Problem description is also incomplete.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
if
m deg=%285x-4%29+
m+gef=%287x-8%29+
m+deh=%289y%2B5%29+
find the values of x and y

Capture

m gef=%287x-8%29 and m+deh=%289y%2B5%29 is same, so

7x-8+=9y%2B5....solve for y
7x-8+-5=9y
y=%287x-13%29%2F9.......eq.1

if m deg=%285x-4%29, we also know that m +deg=+180-deh, so we have

%285x-4%29=180-%289y%2B5%29.....solve for y
5x-4=180-9y-5
9y=180-5%2B4-5x
9y=179-5x
y=%28179-5x%29%2F9....eq.2


from eq.1 and eq.2 we have
%287x-13%29%2F9=%28179-5x%29%2F9
7x-13=179-5x
7x%2B5x=179%2B13
12x=192
x=192%2F12
x=16

go to
y=%287%2A16-13%29%2F9.......eq.1, substitute x
y=99%2F9
y=11



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
if m deg=(5x-4) m gef=(7x-8) m deh=(9y+5) find the values of x and y

If the diagram that woman has is correct, then in no way should you do it the way she does. Who wants to solve for
a variable and then work with fractions that that solved-variable produces? Certainly NOT anyone I know!!!

Again, if diagram is correct, then ∡s DEG & GEF are supplementary. Therefore, ∡DEG + ∡GEF = 180o
                                                                           5x - 4 + 7x - 8 = 180  
                                                                                   5x + 7x = 180 + 12   
                                                                                       12x = 192 
                                                                                       

Again, if diagram is correct, then ∡s GEF & DEH are vertical, and so, are congruent. Hence, ∡GEF = ∡DEH
                                                                                          7x - 8 = 9y + 5   
                                                                                       7(16) - 8 = 9y + 5 -- Substituting 16 for x
                                                                                         112 - 8 = 9y + 5
                                                                                         104 - 5 = 9y
                                                                                              99 = 9y