Question

if →ik and →ln are parallel lines and m∠nmo = 41°, what is m∠lmo?

Explanation:

Step1: Recall the property of supplementary angles

When two angles form a linear pair (they are adjacent and their non - common sides form a straight line), they are supplementary. That is, the sum of their measures is \(180^{\circ}\). In this case, \(\angle NMO\) and \(\angle LMO\) form a linear pair.

Step2: Set up the equation

Let \(m\angle LMO=x\). We know that \(m\angle NMO = 41^{\circ}\), and since \(m\angle NMO+m\angle LMO = 180^{\circ}\) (supplementary angles), the equation is \(41^{\circ}+x=180^{\circ}\).

Step3: Solve the equation for \(x\)

Subtract \(41^{\circ}\) from both sides of the equation: \(x=180^{\circ}- 41^{\circ}\).

$$x = 139^{\circ}$$

Answer:

\(139^{\circ}\)