Option B:
The value of x is [tex]-\frac{11}{2}[/tex].
Solution:
JKLM is an isosceles trapezoid.
JK and LM are legs which are congruent sides and KL is the base.
JK = 8x - 9, KL = 7x + 10 and LM = 10x + 2
By the definition of isosceles trapezoid:
⇒ JK = LM
[tex]\Rightarrow 8x-9=10x+2[/tex]
Add 9 both sides.
[tex]\Rightarrow 8x-9+9=10x+2+9[/tex]
[tex]\Rightarrow 8x=10x+11[/tex]
Subtract 10x from both sides.
[tex]\Rightarrow 8x-10x=10x+11-10x[/tex]
[tex]\Rightarrow -2x=11[/tex]
Divide by -2 on both sides.
[tex]$\Rightarrow \frac{ -2x}{-2} =\frac{11}{-2}[/tex]
[tex]$\Rightarrow x = -\frac{11}{2}[/tex]
The value of x is [tex]-\frac{11}{2}[/tex].
Option B is the correct answer.
