Questions: Look at this diagram: If I K and L N are parallel lines and m angle N M J=119°, what is m angle I J M ?

Solution Steps

We are given that lines $IK$ and $LN$ are parallel, and the measure of angle $\angle NMJ$ is $119^\circ$.

Since $IK \parallel LN$ and $MJ$ is a transversal, $\angle NMJ$ and $\angle JMO$ are consecutive interior angles. Consecutive interior angles on the same side of the transversal are supplementary.

Since consecutive interior angles are supplementary: $$\angle NMJ + \angle JMO = 180^\circ$$ Given $\angle NMJ = 119^\circ$: $$119^\circ + \angle JMO = 180^\circ$$ $$\angle JMO = 180^\circ - 119^\circ$$ $$\angle JMO = 61^\circ$$

Final Answer