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

Jazlyn Durham

Jazlyn Durham



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


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
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∘

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?