GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 05 Aug 2020, 08:59 ### GMAT 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

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # The figure shows that AB=AC=DE=DC, ∠BAC = 30o, ∠PED = 50o and △ABC an

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 9261
GMAT 1: 760 Q51 V42
GPA: 3.82
The figure shows that AB=AC=DE=DC, ∠BAC = 30o, ∠PED = 50o and △ABC an  [#permalink]

### Show Tags 00:00

Difficulty:   25% (medium)

Question Stats: 88% (02:21) correct 13% (02:45) wrong based on 16 sessions

### HideShow timer Statistics

[GMAT math practice question]

Attachment: Picture1.png [ 6.07 KiB | Viewed 237 times ]

The figure shows that $$AB=AC=DE=DC, ∠BAC = 30^o, ∠PED = 50^o$$ and $$△ABC$$ and $$△CDE$$ are congruent. What is the measure of angle $$∠ABP = x$$?

A. $$10^o$$

B. $$15^o$$

C. $$20^o$$

D. $$25^o$$

E. $$30^o$$

_________________

Originally posted by MathRevolution on 06 Jul 2020, 00:40.
Last edited by Bunuel on 12 Jul 2020, 08:54, edited 2 times in total.
Director  G
Joined: 16 Feb 2015
Posts: 657
Location: United States
Re: The figure shows that AB=AC=DE=DC, ∠BAC = 30o, ∠PED = 50o and △ABC an  [#permalink]

### Show Tags

MathRevolution , Figure is missing.

Please edit the question with figure.
Math Expert V
Joined: 02 Sep 2009
Posts: 65807
Re: The figure shows that AB=AC=DE=DC, ∠BAC = 30o, ∠PED = 50o and △ABC an  [#permalink]

### Show Tags

MathRevolution wrote:
[GMAT math practice question]

The figure shows that $$AB=AC=DE=DC, ∠BAC = 30^o, ∠PED = 50^o$$ and $$△ABC$$ and $$△ABC$$ are congruent. What is the measure of angle $$∠ABP = x$$?

A. $$10^o$$

B. $$15^o$$

C. $$20^o$$

D. $$25^o$$

E. $$30^o$$

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 9261
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The figure shows that AB=AC=DE=DC, ∠BAC = 30o, ∠PED = 50o and △ABC an  [#permalink]

### Show Tags

=>

$$∠ABC = ∠DEC = \frac{(180° - 30°) }{ 2} = 75°.$$

Then we have $$∠BEC = 180° – ( 50° + 75° ) = 55°.$$

Since exterior $$∠BEC$$ of triangle $$ABE$$ is the sum of non-adjacent interior angles, $$30°$$, and $$x$$, we have $$x + 30° = 55°$$ or $$x = 25°.$$

Therefore, D is the correct answer.
_________________ Re: The figure shows that AB=AC=DE=DC, ∠BAC = 30o, ∠PED = 50o and △ABC an   [#permalink] 07 Jul 2020, 23:22

# The figure shows that AB=AC=DE=DC, ∠BAC = 30o, ∠PED = 50o and △ABC an  