Final answer:
To find m∠ L in △ LMN with LM congruent to NL and m∠ N=44°, we use the fact that the sum of angles in a triangle is 180° to calculate that m∠ L is 68°.
Step-by-step explanation:
The question pertains to solving for an angle in an isosceles triangle. In △ LMN, lines LM and NL are congruent, which means angles L and M are also congruent as they are the base angles of the isosceles triangle. Given that the measure of angle N (m∠ N) is 44°, we can determine the measure of angle L (m∠ L) using the fact that the sum of angles in any triangle is 180°.
To find the measure of angle L, we subtract the given angle from 180° and then divide by 2 because the triangle is isosceles and thus angles L and M are equal.
m∠ L = (180° - m∠ N) / 2
m∠ L = (180° - 44°) / 2 = 68°