Question

look at this diagram: if ↔{ik} and ↔{ln} are parallel lines and ( mangle ijh = 126^circ ), what is ( mangle lmj )?

Explanation:

Step1: Find the measure of the adjacent angle to \(\angle IJH\)

Since \(\angle IJH\) and \(\angle KJM\) are vertical angles, \(\angle KJM=\angle IJH = 126^{\circ}\). And \(\angle KJM\) and \(\angle LMK\) are same - side interior angles. For parallel lines \(IK\) and \(LN\) cut by a transversal, \(\angle KJM+\angle LMK = 180^{\circ}\). So \(\angle LMK=180^{\circ}-\angle KJM\). Substituting \(\angle KJM = 126^{\circ}\), we get \(\angle LMK = 180 - 126=54^{\circ}\).

Step2: Use the property of vertical angles

\(\angle LMJ\) and \(\angle LMK\) are vertical angles. Vertical angles are equal. So \(m\angle LMJ=m\angle LMK\).

Answer:

\(54\)