It is given that ΔABC ~ ΔDFE, $\angle$A =$30^\circ$, $\angle$C = $50^\circ$, AB = 5 cm, AC = 8 cm and DF = 7.5 cm. Then, the following is true ______.

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It is given that ΔABC ~ ΔDFE, $\angle$A =$30^\circ$, $\angle$C = $50^\circ$, AB = 5 cm, AC = 8 cm and DF = 7.5 cm. Then, the following is true DE = 12 cm, $\angle$F = $100^\circ$. Explanation: Given, ∆ABC ~ ∆DFE, Then $\angle$A = $\angle$D = $30^\circ$, $\angle$C = $\angle$E = $50^\circ$ $\therefore$ $\angle$B = $\angle$F = $180^\circ$ – ($30^\circ$ + $50^\circ$) = $100^\circ$ Also, AB = 5 cm, AC = 8 cm And DF = 7.5 cm $\therefore$ `("AB")/("DF") = ("AC")/("DE") \implies $\frac{5}{7}$.5 = 8/("DE") $\therefore$ DE = (8 xx 7.5)/5` = 12 cm Hence, DE = 12 cm, $\angle$F = $100^\circ$ [Solution diagram: 270199_solution_1.png]

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