If ΔABC ~ΔDFE, ∠A = 30°,
Question:

If ΔABC ~ΔDFE, ∠A = 30°, ∠C = 50°, AB = 5 cm, AC = 8 cm and OF = 7.5 cm. Then, which of the following is true?

(a) DE =12 cm, ∠F =50°

(b) DE = 12 cm, ∠F =100°

(c) EF = 12 cm, ∠D = 100°

(d) EF = 12 cm,∠D =30°

Solution:

(b) Given, AABC ~ ADFE, then ∠A = ∠D = 30°, ∠C ∠E = 50°

$\therefore \quad \angle B=\angle F=180^{\circ}-\left(30^{\circ}+50^{\circ}\right)=100^{\circ}$

Also, $\quad A B=5 \mathrm{~cm}, A C=8 \mathrm{~cm}$ and $D F=7.5 \mathrm{~cm}$

$\therefore$ $\frac{A B}{D F}=\frac{A C}{D E}$

$\Rightarrow$ $\frac{5}{7.5}=\frac{8}{D E}$

$\therefore$ $D E=\frac{8 \times 7.5}{5}=12 \mathrm{~cm}$

Hence, $D E=12 \mathrm{~cm}, \angle F=100^{\circ}$