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Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Location: India
WE:Education (Education)
ABCDE is a regular pentagon with a point O in between, such that OCD
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11 May 2021, 07:35
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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Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Location: India
WE:Education (Education)
Re: ABCDE is a regular pentagon with a point O in between, such that OCD
[#permalink]
12 May 2021, 22:18
12 May 2021, 22:18
1
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°
_________________
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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ABCDE is a regular pentagon with a point O inside.png [ 6.23 KiB | Viewed 1431 times ]
_________________
I hope this helps!
Regards:
Karun Mendiratta
Founder and Quant Trainer
Prepster Education, Delhi, India
https://www.instagram.com/prepster_education/
Regards:
Karun Mendiratta
Founder and Quant Trainer
Prepster Education, Delhi, India
https://www.instagram.com/prepster_education/
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Re: ABCDE is a regular pentagon with a point O in between, such that OCD
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06 Feb 2023, 06:46
06 Feb 2023, 06:46
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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