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ABCDE is a regular pentagon with a point O in between, such that OCD

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ABCDE is a regular pentagon with a point O in between, such that OCD [#permalink] New post   11 May 2021, 07:35
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ABCDE is a regular pentagon with a point O inside it, such that OCD is an equilateral triangle. What is the measure of angle AEO (in degrees)?

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Re: ABCDE is a regular pentagon with a point O in between, such that OCD [#permalink] New post   12 May 2021, 22:18
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Since ABCDE is a regular pentagon and OCD is an equilateral triangle
AB = BC = CD = DE = EA = OC = OD

We know, each interior angle of a regular pentagon is 108°
∠CDE = ∠ODC + ∠ODE
108° = 60° + ∠ODE
∠ODE = 48°

Now, In triangle ODE, OD = DE i.e. ∠DEO = ∠DOE = x
∠ODE + ∠DEO + ∠DOE = 180°
48° + 2x = 180°
x = 66°

Also, ∠DEA = ∠OED + ∠AEO
108° = 66° + ∠AEO
∠AEO = 42°
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Re: ABCDE is a regular pentagon with a point O in between, such that OCD [#permalink] New post   06 Feb 2023, 06:46
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Re: ABCDE is a regular pentagon with a point O in between, such that OCD [#permalink]
06 Feb 2023, 06:46
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