Question

lines cd, ab, gb, and fe are shown. m∠mbh = 70°, m∠fkd = 60°, and m∠gjc=(2x - 18)°. what value of x shows that line ab is parallel to line cd? o 39 o 44 o 136 o 141

Explanation:

Step1: Identify corresponding - angles

When \(AB\parallel CD\), \(\angle GJC\) and \(\angle MBH\) are corresponding angles. For parallel lines, corresponding angles are equal.

Step2: Set up the equation

Since \(\angle GJC=\angle MBH\) for \(AB\parallel CD\), we set up the equation \(2x - 18=70\).

Step3: Solve the equation for \(x\)

Add 18 to both sides of the equation: \(2x=70 + 18\), so \(2x=88\). Then divide both sides by 2: \(x=\frac{88}{2}=44\).

Answer:

44