Question

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?
A. `DE=12 cm, angle F=50^(@)`
B. `DE=12 cm, angle F=100^(@)`
C. `EF=12 cm, angle D=100^(@)`
D. `EF=12 cm, angle D=30^(@)`

Answer 1

Correct Answer - B
`angle B=180^(@)-(30^(@)+50^(@))=100^(@)`
Since `Delta ABC~Delta DEF`, we have `angle D= angleA=30^(@), angle F= angle B=100^(@) and angle E= angle C=50^(@)`. Let the `DE=x` cm. then,
`(AB)/(DF)=(AC)/(DE)rArr (5)/(7.5)=(8)/(x)`
`:. 5x=8xx7.5 rArr x(8xx7.5)/(5) =12`
Hence, `DE=12 cm and angle F=100^(@)`