Question

solve for x.
j (10x - 26)°
k (7x + 7)°
x =

Explanation:

Step1: Identify angle - relationship

Assume lines FG and HI are parallel, and DE is a transversal. The angles \((10x - 26)^{\circ}\) and \((7x + 7)^{\circ}\) are corresponding angles. Corresponding angles formed by a transversal intersecting two parallel lines are congruent. So, \(10x-26 = 7x + 7\).

Step2: Solve the equation for x

Subtract \(7x\) from both sides: \(10x-7x-26=7x - 7x+7\), which simplifies to \(3x-26 = 7\).

Step3: Isolate the variable term

Add 26 to both sides: \(3x-26 + 26=7 + 26\), getting \(3x=33\).

Step4: Solve for x

Divide both sides by 3: \(x=\frac{33}{3}=11\).

Answer:

11