Question

if ∆ABC ~= ∆FDE and AB=5cm, angle B=40° and angle A=80°, then find the value of DF and angle E​

Answer 1

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Answer 2

Given:

• ∆ABC ≅ ∆FDE
• AB = 5 cm
• ∠B = 40°
• ∠A = 80°

To find:

• DF?
• ∠E?

Solution:

Given that,

∆ABC ≅ ∆FDE

then,

AB = FD

BC = DF

AC = FE

And,

∠ABC = ∠FDE

∠BCA = ∠DEF

∠CAB = ∠EFD

Here, Given that,

• AB = 5 cm
• B = 40°
• A = 80°

So,

∠FDE = 40° [ ∠ABC = ∠FDE ]

∠EFD = 80° [ ∠CAB = ∠EFD ]

FD = 5 cm [ AB = FD ]

We know that,

→ ∠D + ∠E + ∠F = 180° [ Angle sum property ]

→ 40° + ∠E + 80° = 180°

→ ∠E + 120° = 180°

→ ∠E = 180° - 120°

→ ∠E = 60°

∴ Hence, ∠DEF = 60° and DF = 5 cm.