Question

If ∆ABC ∼ ∆DFE, ∠A = 30°, ∠C = 50°, AB = 5 cm, AC = 8 cm and DF = 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°

Answer 1

Given: ∆ABC ∼ ∆DFE,

As ∆ABC ∼ ∆DFE so, by the property of Corresponding angles of similar triangles,

We have,

∠A = ∠D = 30° (Corresponding angles)

∠C = ∠E = 50° (Corresponding angles)

We know that sum of angles of a triangle = 180°

So,

∴ ∠B = ∠F = 180°- (30° + 50°) = 100°

Also Given,

AB = 5 cm,

AC = 8 cm and

DF = 7.5 cm

Hence,

DE = 12 cm, and ∠F = 100°