GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
ABCDE is a regular pentagon with a point O in between, such that OCD
[#permalink]
11 May 2021, 07:35
11 May 2021, 07:35
1
2
Bookmarks
00:00
Question Stats:
57% (02:18) correct
42% (02:38) wrong based on 7 sessions
Hide Show timer Statistics
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)?
Show: ::
42
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
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°
Attachments
ABCDE is a regular pentagon with a point O inside.png [ 6.23 KiB | Viewed 3585 times ]
General Discussion
Re: ABCDE is a regular pentagon with a point O in between, such that OCD
[#permalink]
06 Feb 2023, 06:46
06 Feb 2023, 06:46
Hello from the GRE Prep Club BumpBot!
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).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
