Question

solve for x. x =

Explanation:

Step1: Use the property of corresponding angles

Since \(IJ\parallel KL\), \((7x - 65)^{\circ}\) and \(56^{\circ}\) are corresponding angles. Corresponding angles are equal. So, \(7x-65 = 56\).

Step2: Solve the equation for \(x\)

Add \(65\) to both sides of the equation: \(7x=56 + 65\). Then \(7x=121\). Divide both sides by \(7\): \(x=\frac{121}{7}\). Wait, no, there's a mistake. Wait, \(IJ\parallel KL\), and \((7x - 65)\) and \(56\) are actually same - side exterior and interior angles? No, no, they are consecutive interior angles. Wait, no, no. Wait, \(IJ\parallel KL\), and \(GH\) is a transversal. \((7x - 65)\) and \(56\) are supplementary (consecutive interior angles). So \(7x-65+56 = 180\).

Step3: Simplify the equation

\(7x-9 = 180\). Add \(9\) to both sides: \(7x=180 + 9=189\).

Step4: Solve for \(x\)

Divide both sides by \(7\): \(x=\frac{189}{7}=27\).

Answer:

\(27\)