Question

solve for x.

x =

Explanation:

Step1: Use the property of corresponding angles

When two parallel lines \(FG\) and \(HI\) are cut by a transversal \(DE\), the sum of the angle \((2x - 15)^{\circ}\) and \(59^{\circ}\) is \(180^{\circ}\) (they are same - side interior angles). So, we have the equation \((2x-15)+59 = 180\).

Step2: Simplify the left - hand side of the equation

Simplify \((2x-15)+59\) to get \(2x+( - 15 + 59)=2x + 44\). So the equation becomes \(2x+44 = 180\).

Step3: Solve for \(x\)

Subtract \(44\) from both sides of the equation \(2x+44 = 180\). We get \(2x=180 - 44\), so \(2x = 136\). Then divide both sides by \(2\), \(x=\frac{136}{2}\).

Answer:

\(x = 68\)