1. **State the problem:** We have two similar triangles. In the first triangle, angles $\angle L = 55^\circ$ and $\angle J = 100^\circ$ are given. We need to find the measures of angles $\angle E$, $\angle F$, and $\angle G$ in the second triangle. 2. **Recall properties of triangles and similarity:** - The sum of interior angles in any triangle is $180^\circ$. - Similar triangles have corresponding angles equal. 3. **Find the third angle in the first triangle:** $$\angle K = 180^\circ - (\angle L + \angle J) = 180^\circ - (55^\circ + 100^\circ) = 180^\circ - 155^\circ = 25^\circ$$ 4. **Match corresponding angles between the triangles:** Since the triangles are similar, their angles correspond in order. Assuming the order of vertices corresponds, then: - $\angle L$ corresponds to $\angle F$, - $\angle J$ corresponds to $\angle E$, - $\angle K$ corresponds to $\angle G$. 5. **Write the measures for the second triangle:** $$\angle E = 100^\circ$$ $$\angle F = 55^\circ$$ $$\angle G = 25^\circ$$ **Final answer:** - $m \angle E = 100^\circ$ - $m \angle F = 55^\circ$ - $m \angle G = 25^\circ$