SOLUTION: Please help me solve this equation. Find x if {{{ m<LEF= 70, }}} {{{m<DEL= 14+6x,}}} {{{and m <DEF= 13x+7.}}}

Algebra ->  Angles -> SOLUTION: Please help me solve this equation. Find x if {{{ m<LEF= 70, }}} {{{m<DEL= 14+6x,}}} {{{and m <DEF= 13x+7.}}}      Log On


   

Question 725955: Please help me solve this equation.
Find x if +m%3CLEF=+70%2C+ m%3CDEL=+14%2B6x%2C and+m+%3CDEF=+13x%2B7.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
This is hard to do without the diagram but I am guessing that angles LEF and DEL are adjacent angles. (Adjacent angles are angles with the same vertex, a shared/common side and non-overlapping interiors.)

If I am right then there is a relationship between the measures of the two adjacent angles and the measure of the "big" angle formed by the vertex and the two sides of the adjacent angles that are not shared. (In this case the "big" angle would be angle DEF.) This relationship is that the sum of the measures of the adjacent angles is equal to the measure of the "big" angle.

So:
(70) + (14+6x) = 13x + 7
Now we just solve for x. Adding like terms:
6x + 84 = 13x + 7
Subtracting 6x from each side:
84 = 7x + 7
Subtracting 7 from each side:
77 = 7x
Dividing by 7:
11 = x