It is given tha , = 30^ , =40^ , AB= 5 cm , AC=8 cm and DF = 7.5 cm. Then, which of the following is true :

It is given tha , = 30^ , =40^ , AB= 5 cm , AC=8 cm and DF = 7.5 …

MCQ

It is given tha $\triangle\text{ABC}\sim\triangle\text{DFE},\angle\text{A} = 30^\circ,\angle\text{C}=40^\circ , \text{AB}= 5\text{ cm} , \text{AC}=8\text{ cm}$ and $DF = 7.5\ cm$. Then, which of the following is true :

✓
$\angle\text{F}=110^\circ , \text{DE}=12\text{ cm}$
B
$\angle\text{D}=30^\circ , \text{EF}=12\text{ cm}$
C
$\angle\text{F}=110^\circ , \text{EF}=12\text{ cm}$
D
$\angle\text{F}=40^\circ , \text{DE}=12\text{ cm}$

✓

Answer

Correct option: A.

$\angle\text{F}=110^\circ , \text{DE}=12\text{ cm}$

In $\triangle\text{ABC},\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
$\Rightarrow30^\circ+40^\circ\angle\text{B}=180^\circ$
$\Rightarrow\angle\text{B}=180^\circ$
$\text{since }\triangle\text{ABC}\sim\triangle\text{DFE}$
$\therefore\angle\text{B}=\angle\text{F}=110^\circ$
$\frac{\text{DF}}{\text{DE}}=\frac{\text{AB}}{\text{AC}} $
$\Rightarrow\frac{7.5}{\text{DE}}=\frac{5}{8}$
$\Rightarrow\text{DE}=12\text{ cm}$