AB = BC = CD = DE = EF = FG = GA. Then, ∠DAE...

Jazlyn Durham

Jazlyn Durham

Answered

2022-12-31

AB = BC = CD = DE = EF = FG = GA. Then, ∠DAE is approximately
15 degrees
30 degrees
20 degrees
25 degrees

Answer & Explanation

Rihanna Gamble

Rihanna Gamble

Expert

2023-01-01Added 12 answers

∠EAD=α, then, ∠AFG=α and also ∠ACB=α.
Hence ∠CBD=2α (exterior angle to ΔABC)
CB = CD, hence ∠CDB=2α∠FGC=2α (exterior angle to ΔAFG).
Since GF = EF, ∠FEG=2α
Now, ∠DCE=∠DEC=β (say)
Then, ∠DEF=β−2α
Since, ∠DCB=180∘−(α+β)
Therefore, on ΔDCB,
180∘−(α+β)+2α+2α=180∘ or β=3α
Further ∠EFD=∠EDF=γ (say)
Then, ∠EDC=γ−2α
If CD and EF meet at P,
then ∠FPD=180∘−5α
[∵β=3α]
Now in ΔPED, 180∘−5α+γ+2α=180∘ or γ=3α
Therefore, in ΔEFD,
α+2γ=180∘ or α+6α=180∘ or α=26∘
or approximately 25∘

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