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 ?

Transcript text: easyCBM - Taking M. Papa's Freezeria - P 444455645 Dysthymia: more th... My IXL Learning Asses: $\square$ D. 4 Transversals of parallel lines: find angle measures WB9 Look at this diagram: If $\overleftrightarrow{I K}$ and $\overleftrightarrow{L N}$ are parallel lines and $m \angle N M J=119^{\circ}$, what is $m \angle I J M ?$ $\square$

Solution

Solution Steps

Step 1: Identify the given information

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

Step 2: Identify the relationship between angles

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.

Step 3: Calculate the measure of $ \angle JMO $

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

The measure of $ \angle JMO $ is $ 61^\circ $.

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