Question

look at this diagram: diagram with lines km, hj, and transversal ng intersecting at l and i if hj and km are parallel lines and m∠mli= 114°, what is m∠jig? blank° submit

Explanation:

Step1: Identify angle relationship

Since \( HJ \parallel KM \) and \( NG \) is a transversal, \( \angle MLI \) and \( \angle JIG \) are same - side interior angles? No, wait, actually \( \angle MLI \) and \( \angle JIG \) are supplementary? Wait, no, let's look at the positions. \( \angle MLI \) and \( \angle JIG \): since \( HJ\parallel KM \), and \( NG \) is a transversal, \( \angle MLI \) and \( \angle JIG \) are same - side? Wait, no, \( \angle MLI \) and \( \angle JIG \): actually, \( \angle MLI \) and \( \angle JIG \) are supplementary? Wait, no, let's think again. The sum of same - side interior angles is \( 180^{\circ} \). Wait, \( \angle MLI \) and \( \angle JIG \): let's see, \( KM\parallel HJ \), transversal \( NG \). So \( \angle MLI \) and \( \angle JIG \): are they same - side interior angles? Let's check the lines. \( KM \) is vertical, \( HJ \) is vertical, so they are parallel. The transversal is \( NG \). So \( \angle MLI \) and \( \angle JIG \): \( \angle MLI \) is at \( L \) between \( KM \) and \( NG \), \( \angle JIG \) is at \( I \) between \( HJ \) and \( NG \). Since \( KM\parallel HJ \), \( \angle MLI \) and \( \angle JIG \) are same - side interior angles? Wait, no, actually, \( \angle MLI \) and \( \angle JIG \): the sum of same - side interior angles is \( 180^{\circ} \). Wait, but \( \angle MLI = 114^{\circ} \), so \( \angle JIG=180 - 114 \).

Step2: Calculate the measure of \( \angle JIG \)

We know that for two parallel lines cut by a transversal, same - side interior angles are supplementary. So \( m\angle MLI + m\angle JIG=180^{\circ} \).
Given \( m\angle MLI = 114^{\circ} \), then \( m\angle JIG=180^{\circ}- 114^{\circ} \)
\( 180 - 114 = 66 \)

Answer:

\( 66 \)