Question

look at this diagram: diagram with lines hj, km, and gn intersecting at i and l if \overleftrightarrow{hj} and \overleftrightarrow{km} are parallel lines and m\angle kln = 131\degree, what is m\angle mln?

Explanation:

Step1: Identify Angle Relationship

Since \( \overleftrightarrow{HJ} \parallel \overleftrightarrow{KM} \) and \( \overleftrightarrow{GN} \) is a transversal, \( \angle KLM \) and \( \angle KLN \) are supplementary? Wait, no—wait, \( \angle KLN = 131^\circ \), and we need \( \angle MLN \). Wait, actually, \( \angle KLM \) (wait, the diagram: \( HJ \parallel KM \), so consecutive interior angles? Wait, no, \( \angle KLN \) and \( \angle MLN \) are supplementary? Wait, no, let's see: \( \angle KLN \) and \( \angle MLN \) form a linear pair? Wait, no, \( HJ \parallel KM \), so the corresponding angles or same - side interior angles. Wait, \( \angle KLN = 131^\circ \), and \( \angle MLN \) and \( \angle KLN \) are supplementary? Wait, no, actually, since \( HJ \parallel KM \), the angle \( \angle KLN \) and \( \angle MLN \): wait, \( \angle KLN \) is an angle, and \( \angle MLN \) is adjacent? Wait, no, let's think again. If \( HJ \parallel KM \), then the angle \( \angle KLN \) and \( \angle MLN \): the sum of a linear pair is \( 180^\circ \). Wait, \( \angle KLN = 131^\circ \), so \( m\angle MLN=180^\circ - 131^\circ \).

Step2: Calculate the Angle

\( m\angle MLN = 180^\circ-131^\circ = 49^\circ \)

Answer:

\( 49^\circ \)