Decide whether the triangles are similar. If so, determine the appropriate expression to solve for x.Triangles ABC and EDF, where triangle ABC has angle A measuring 47 degrees, angle C measuring 62 degrees, side AC labeled as y, side AB labeled as w, and side BC labeled as x and triangle EDF has angle D measuring 71 degrees, angle E measuring 47 degrees, side DE labeled z, side EF labeled u, and side DF labeled r The triangles are not similar; no expression for x can be found. ΔABC ~ ΔDEF; x equals r times w over u ΔABC ~ ΔEDF; x equals r times w over u ΔABC ~ ΔEDF; x equals r times w over z

Answer:Δ ABC is similar to Δ EDF and [tex]x = r\frac{w}{z}[/tex]Step-by-step explanation:In Δ ABC, ∠ A = 47° and ∠ C = 62°  So, ∠ B = 180° - 62° - 47° = 71° Again, in Δ EDF, ∠ D = 71°, and ∠ E = 47°  So, ∠ F = 180° - 71° - 47° = 62° Hence, Δ ABC is similar to Δ EDF Now, for two similar triangles the ratio of corresponding sides will be in the same ratio. So, [tex]\frac{BC}{DF} = \frac{AB}{ED}[/tex] ⇒ [tex]\frac{x}{r} = \frac{w}{z}[/tex] ⇒ [tex]x = r\frac{w}{z}[/tex]. Therefore, the correct option is 3. (Answer)