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? 39 44 136 141

Explanation:

Step1: Identify corresponding angles

When \(AB\parallel CD\), \(\angle GJC\) and \(\angle MHB\) are corresponding angles. First, find \(\angle MHB\). Since \(\angle MBH = 70^{\circ}\) and \(\angle FKD=60^{\circ}\) are not relevant to the parallel - line relationship for this pair of corresponding angles. The angle \(\angle MHB\) and \(\angle GJC\) are equal when \(AB\parallel CD\). And \(\angle MHB\) and \(\angle MBH\) are adjacent angles on a straight - line, so \(\angle MHB = 180^{\circ}-\angle MBH\). But we can also use the fact that for parallel lines \(AB\) and \(CD\), \(\angle GJC\) and \(\angle MHB\) are equal. We know that \(\angle GJC\) and the angle adjacent to \(\angle MBH\) (let's call it \(\angle MHB\)) are corresponding angles. Since \(\angle GJC\) and \(\angle MHB\) are equal for \(AB\parallel CD\), and \(\angle MHB\) and \(\angle MBH\) are supplementary. We can also use the property of corresponding angles directly. When \(AB\parallel CD\), \(\angle GJC\) and the angle corresponding to it (let's assume the relevant angle) are equal. We know that \(\angle GJC\) should be equal to the angle corresponding to it for parallel lines. So we set up the equation based on the equality of corresponding angles.

Step2: Set up the equation

If \(AB\parallel CD\), then \(\angle GJC\) and the corresponding angle are equal. We know that \(\angle GJC=(2x - 18)^{\circ}\). For parallel lines, we assume the relevant corresponding - angle relationship. Since the sum of angles on a straight - line formed by the transversal and one of the parallel lines is not needed here, we just set \(\angle GJC\) equal to the corresponding angle value. We know that for parallel lines, the corresponding angles are equal. So \(2x-18 = 70\) (assuming the correct corresponding - angle relationship).

Step3: Solve the equation

Add 18 to both sides of the equation \(2x-18 = 70\):

$$2x=70 + 18$$

$$2x=88$$

Divide both sides by 2:

$$x = 44$$

Answer:

B. 44