It is given that ΔABC ∼ ΔDFE. If ∠A = 30°, ∠C = 50°, AB = 5 cm, AC = 8 cm and DF = 7.5 cm, then which of the following is true?

1. DE = 12 cm, ∠F = 50°

2. DE = 12 cm, ∠F = 100°

3. EF = 12 cm, ∠D = 100°

4. EF = 12 cm, ∠D = 30°

Given,

∠A = 30°

∠C = 50°

In triangle ABC,

∠A + ∠B + ∠C = 180°

∠B = 180° - (∠A + ∠C)

∠B = 180° - (30° + 50°)

∠B = 180° - 80°

∠B = 100°.

As the triangles are similar, the corresponding angles will be equal.

So, ∠F = ∠B = 100°

Since the triangles are similar, the ratio of corresponding sides is proportional,

$\Rightarrow \dfrac{AB}{DF} = \dfrac{AC}{DE} = \dfrac{BC}{FE} \\[1em] \text{Let's consider} \\[1em] \Rightarrow \dfrac{AB}{DF} = \dfrac{AC}{DE} \\[1em] \Rightarrow \dfrac{5}{7.5} = \dfrac{8}{DE} \\[1em] \Rightarrow DE = \dfrac{8 \times 7.5}{5} \\[1em] \Rightarrow DE = \dfrac{60}{5} \\[1em] \Rightarrow DE = 12 \text{ cm.}$

DE = 12 cm, ∠F = 100°

Hence, option 2 is the correct option.