Question

lines j and k are parallel. they are intersected by the transversals l and m. what is the value of x? a. 72° b. 78° c. 87°

Explanation:

Step1: Use property of parallel lines

When two parallel lines are intersected by a transversal, corresponding - angles are equal and same - side interior angles are supplementary. The angle adjacent to the \(72^{\circ}\) angle on the transversal \(m\) and the \(93^{\circ}\) angle are same - side interior angles. The angle adjacent to the \(72^{\circ}\) angle is \(180 - 72=108^{\circ}\).

Step2: Find the value of \(x\)

Since the lines \(j\) and \(k\) are parallel and \(l\) and \(m\) are transversals, the \(87^{\circ}\) angle and the angle \(x\) are corresponding angles. Corresponding angles formed by two parallel lines and a transversal are equal. So \(x = 87^{\circ}\).

Answer:

C. \(87^{\circ}\)