Question

look at this diagram: if km and np are parallel lines and m∠poq = 127°, what is m∠mlr?

Explanation:

Step1: Find the measure of the adjacent angle to ∠POQ

Since ∠POQ and ∠NOL are vertical angles, ∠NOL = ∠POQ = 127°. And ∠NOL and ∠MLO are supplementary angles (because \(NP\parallel KM\) and \(QJ\) is a transversal, consecutive - interior angles are supplementary). The formula for supplementary angles is \(m\angle NOL+m\angle MLO = 180^{\circ}\).
Substitute \(m\angle NOL = 127^{\circ}\) into the formula: \(127^{\circ}+m\angle MLO = 180^{\circ}\).
Solve for \(m\angle MLO\): \(m\angle MLO=180^{\circ}- 127^{\circ}=53^{\circ}\).

Step2: Use the vertical - angle relationship

Since ∠MLJ and ∠MLO are vertical angles. By the vertical - angle theorem (vertical angles are equal), \(m\angle MLJ=m\angle MLO\).

Answer:

\(53^{\circ}\)