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555-605 (Medium)|   Geometry|      
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MathRevolution
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The figure shows that AB=AC=DE=DC, ∠BAC = 30o, ∠PED = 50o and △ABC an Updated on: 12 Jul 2020, 09:54
Originally posted by MathRevolution on 06 Jul 2020, 01:40.
Last edited by Bunuel on 12 Jul 2020, 09:54, edited 2 times in total.
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73% (02:53) correct 27% (02:56) wrong based on 103 sessions

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[GMAT math practice question]

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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. \(30^o\)
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D
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The figure shows that AB=AC=DE=DC, ∠BAC = 30o, ∠PED = 50o and △ABC an 06 Jul 2020, 03:55
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MathRevolution , Figure is missing.

Please edit the question with figure.
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Bunuel
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The figure shows that AB=AC=DE=DC, ∠BAC = 30o, ∠PED = 50o and △ABC an 06 Jul 2020, 03:56
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MathRevolution
[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. \(30^o\)
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Could you please add the image? It's missing now. Thank you!
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The figure shows that AB=AC=DE=DC, ∠BAC = 30o, ∠PED = 50o and △ABC an 08 Jul 2020, 00:22
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=>

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

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.
Answer: D
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The figure shows that AB=AC=DE=DC, ∠BAC = 30o, ∠PED = 50o and △ABC an 07 Jan 2023, 01:54
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MathRevolution

how angle ABC = ANGLE DEC
can you please elaborate ?
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The figure shows that AB=AC=DE=DC, ∠BAC = 30o, ∠PED = 50o and △ABC an 18 Jan 2023, 21:10
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Extend the straight line DE to lie on AB, lets say at Y. ∠YEB=∠PED=50(vertically opp angles). ∠BAC=∠EDC=30. Therefore ∠DEC=∠DCE=75.
∠DEC=∠AEY=75 (vertically opp angles). Therefore, In △AEB, ∠A=30, ∠E=50+75=125 and ∠x=180-155=25.

Can anyone confirm if this approach is correct?
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