Question

find m∠lnm.
answer attempt 1 out of 2
m∠lnm = °
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Explanation:

Step1: Identify Triangle Type

The triangle \( \triangle LNM \) has two equal sides (marked with ticks), so it's isosceles with \( LM = MN \). Thus, \( \angle L = \angle N \)? Wait, no—wait, in an isosceles triangle, the angles opposite equal sides are equal. Wait, the sides with ticks: \( LM \) and \( MN \)? Wait, no, looking at the diagram, the sides \( LM \) and \( LN \)? Wait, no, the markings: one on \( LM \) and one on \( MN \)? Wait, no, the triangle: vertices L, M, N. The side from L to M has a tick, and from M to N has a tick? Wait, no, maybe \( LM = LN \)? Wait, no, the angle at L is \( 44^\circ \). Wait, in an isosceles triangle, if two sides are equal, the base angles are equal. Wait, let's correct: in \( \triangle LNM \), if \( LM = MN \), then the angles opposite them: angle at N (opposite LM) and angle at L (opposite MN)? Wait, no, vertex labels: L, M, N. So sides: LM, MN, NL. The ticks: LM and MN? Wait, no, the diagram: from L to M, a tick; from M to N, a tick? Wait, no, maybe \( LM = LN \)? Wait, no, the angle at L is \( 44^\circ \). Wait, actually, in an isosceles triangle, the angles opposite the equal sides are equal. So if \( LM = MN \), then angle at L (opposite MN) and angle at N (opposite LM) are equal? Wait, no, let's list the sides:

• Side opposite \( \angle L \): \( MN \)
• Side opposite \( \angle N \): \( LM \)
• Side opposite \( \angle M \): \( LN \)

If \( LM = MN \) (marked with ticks), then \( \angle L = \angle N \). Wait, but \( \angle L \) is \( 44^\circ \), so \( \angle N \) (which is \( \angle LNM \)) would also be \( 44^\circ \)? Wait, no, that can't be, because the sum of angles in a triangle is \( 180^\circ \). Wait, maybe I got the equal sides wrong. Wait, maybe the equal sides are \( LM \) and \( LN \)? Wait, no, the ticks: one on \( LM \) and one on \( LN \)? Wait, the diagram shows: from L to M, a tick; from M to N, a tick? Wait, no, the user's diagram: "the side from L to M has a tick, and from M to N has a tick"? Wait, no, looking at the triangle: L at the bottom, M at the top, N at the right. So sides: LM (left side, tick), MN (top side, tick), and LN (bottom-right side). Wait, no, maybe the equal sides are LM and LN? Wait, no, the tick marks: LM and MN are equal. So \( LM = MN \), so angles opposite: \( \angle N = \angle L \). Wait, \( \angle L = 44^\circ \), so \( \angle N = 44^\circ \)? But then angle at M would be \( 180 - 44 - 44 = 92^\circ \). But that seems possible. Wait, but maybe I misidentified the equal sides. Wait, maybe the equal sides are LM and LN? No, the ticks are on LM and MN. Wait, let's confirm: in an isosceles triangle, two sides are equal, so the angles opposite those sides are equal. So if \( LM = MN \), then \( \angle L = \angle N \). Therefore, \( m\angle LNM = 44^\circ \)? Wait, no, wait: angle at L is \( 44^\circ \), side opposite is MN; angle at N is \( \angle LNM \), side opposite is LM. If LM = MN, then \( \angle L = \angle N \). So yes, \( m\angle LNM = 44^\circ \). Wait, but that seems too simple. Wait, maybe the equal sides are LM and LN? Then angle at M and angle at N would be equal. But the tick is on LM and MN. Wait, the diagram: L---M---N? No, it's a triangle: L, M, N with LM and MN marked equal. So \( \triangle LNM \) is isosceles with \( LM = MN \), so \( \angle L = \angle N = 44^\circ \). Therefore, \( m\angle LNM = 44^\circ \).

Step2: Calculate Angle

Sum of angles in a triangle: \( 180^\circ \). If \( \angle L = 44^\circ \) and \( \angle N = \angle L \) (because \( LM = MN \)), then \( m\angle LNM = 44^\circ \).

Answer:

\( 44 \)