1. **Problem statement:** We have an isosceles triangle LMN with LM = LN. Lines AMB and CLN are parallel. Line DLM is straight. Angle DLN = 118°. We need to find angle AMN and give reasons for each step. 2. Since DLM is a straight line, angle DLM and angle DLN are supplementary. Therefore, $$\angle DLM = 180^\circ - 118^\circ = 62^\circ.$$ *Reason: Supplementary angles on a straight line sum to 180°.* 3. In triangle LMN, LM = LN so triangle LMN is isosceles with equal sides LM and LN. Therefore, angles opposite these sides are equal, so $$\angle LNM = \angle LMN.$$ *Reason: In an isosceles triangle, angles opposite equal sides are equal.* 4. At point L, since line DLM is straight, angle DLM (62°) and angle MLI split the remaining angles around L in triangle LMN. Given $$\angle DLN = 118^\circ,$$ angle MLN must be $$62^\circ$$ as found. 5. Since AMB and CLN are parallel lines and LM is a transversal, alternate interior angles are equal. Hence, $$\angle AMN = \angle MLN = 62^\circ.$$ *Reason: Alternate interior angles are equal when lines are parallel.* 6. Thus, the size of angle AMN is $$62^\circ.$$