Question

it is given that triangle ABC is congruent to triangle DFE . If <A = 30 <C =50 AB = 5 and AC = 8 and if is DF=7.5 then which of the following is true.
A. DE = 12cm , <F = 50°
B) DE = 12cm , <F = 100°
C) EF = 12cm , <D = 100°
D) EF = 12cm , <D = 30°.
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Answer 1

(b) DE = 12cm, ∠F = 1000

I hope this helps you!!

Answer 2

Answer:

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