If `DeltaABC~DeltaDFE,angleA=30,angleC=50^(@)`,AB=5 cm,AC=8 cm and DF=7.5 cm. Then, which of the following is true?

Options

A. `DE=12 cm,angleF=50^(@)`
B. `DE=12cm,angleF=100^(@)`
C. `EF=12cm,angleD=100^(@)`
D. `EF=12cm,angleD=30^(@)`

Answer

B

Explanation

Given, `DeltaABC~DeltaDFE`, then `angleA=angleD=30^(@),angleC=angleE=50^(@)`

`therefore angleB=angleF=180^(@)-(30^(@)+50^(@))=100^(@)`
Also, AB=5cm, AC=8cm and DF=7.5 cm
`therefore(AB)/(DF)=(AC)/(DE)`
`rArr5/7.5=8/(DE)`
`thereforeDE=(8xx7.5)/(5)=12 cm`
Hence, DE=12 cm, `angleF=100^(@)`