It is given that ΔАBС ~ ΔDFE. If $\angle$A = $30^\circ$, $\angle$C = $50^\circ$, AB = 5 cm, AC = 8 cm and DF = 7.5 cm then which of the following is true?

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KollegeApply · Accepted Answer

DE = 12 cm, $\angle$F = $100^\circ$ Explanation: From ΔABC ~ ΔDFE the correspondence is AD, BF, CE. So, $\angle$F = $\angle$B = $180^\circ$ – $30^\circ$ – $50^\circ$ = $100^\circ$ By similarity, corresponding sides are proportional. Use (AC)/(DE) = (AB)/(DF) $\Rightarrow$ DE = (AC xx DF)/(AB) = (8 xx 7.5)/5 = 12 cm Thus, DE = 12 cm and $\angle$F = $100^\circ$.

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