Answer:
[tex]x=28\frac{6}{7}[/tex]
[tex]x \approx 28.857[/tex]
Step-by-step explanation:
It is given that lines (BE) and (CD) are parallel, thus (<AEB) and (EDC) are congruent by alternate interior angles theorem. Moreover, (<A) is shared between the two triangles, therefore it is also congruent. Hence, triangles (ABE) and (ACD) are similar by (angle-angle) similarity.
Side (AD) is composed of segments (AE) and (ED), therefore one can find the total measure of segment (AD):
AD = AE + ED
AD = 7x - 40 + 18
AD = 7x - 22
Side (AC) is made of segments (AB) and (BC), thus one can find the total length of the side (AC) by adding these two segments:
AC = AB + BC
AC = 63 + 7
AC = 70
When two triangles are similar, the ratios of the sides are equal. Therefore, one can make the following statement:
[tex]\frac{AE}{AD}=\frac{AB}{AC}[/tex]
Substitute,
[tex]\frac{7x-40}{7x-22}=\frac{63}{70}[/tex]
Cross products,
[tex]70(7x-40)=63(7x-22)[/tex]
Distribute,
[tex]490x-2800=441x-1386[/tex]
Inverse operations,
[tex]490x-2800=441x-1386[/tex]
[tex]49x-2800=-1386[/tex]
[tex]49x=1414[/tex]
[tex]x=28\frac{6}{7}[/tex]
