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Triangles ABC and ADC are isosceles with AB = BC and AD = DC. Point D

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Bunuel
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Triangles ABC and ADC are isosceles with AB = BC and AD = DC. Point D [#permalink] New post   14 Mar 2019, 01:53
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Triangles ABC and ADC are isosceles with AB = BC and AD = DC. Point D is inside triangle ABC, ∠ABC = 40°, and ∠ADC = 140°. What is the degree measure of ∠BAD?

(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
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D
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globaldesi
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Re: Triangles ABC and ADC are isosceles with AB = BC and AD = DC. Point D [#permalink] New post   14 Mar 2019, 21:18
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Figure drawn as per explained.
Now AB = BC hence angles corresponding will be equal hence \(\angle\) BAC= \(180^{\circ}\)-\(40^{\circ}\) =\(\frac{140^{\circ}}{2}\) = \(70^{\circ}\)
for triangle ADC \(180^{\circ}-40^{\circ}\) =\(\frac{40^{\circ}}{2}\)=\(20^{\circ}\)
thus angle ABD = \(70^{\circ}\)-\(20^{\circ}\) =\(50^{\circ}\)
Thus answer D
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Triangles ABC and ADC are isosceles with AB = BC and AD = DC. Point D [#permalink] New post   Updated on: 14 Mar 2019, 05:30
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Bunuel wrote:
Triangles ABC and ADC are isosceles with AB = BC and AD = DC. Point D is inside 4ABC, ∠ABC = 40°, and ∠ADC = 140°. What is the degree measure of ∠BAD?

(A) 20
(B) 30
(C) 40
(D) 50
(E) 60


Bunuel

draw figure as per given description
IMO angle BAD = 50
IMO D

Originally posted by Archit3110 on 14 Mar 2019, 05:06.
Last edited by Archit3110 on 14 Mar 2019, 05:30, edited 1 time in total.
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Re: Triangles ABC and ADC are isosceles with AB = BC and AD = DC. Point D [#permalink] New post   14 Mar 2019, 05:09
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Archit3110 wrote:
Bunuel wrote:
Triangles ABC and ADC are isosceles with AB = BC and AD = DC. Point D is inside 4ABC, ∠ABC = 40°, and ∠ADC = 140°. What is the degree measure of ∠BAD?

(A) 20
(B) 30
(C) 40
(D) 50
(E) 60


Bunuel

please check highlighted part

Point D is inside 4ABC, ∠ABC = 40°, and ∠ADC = 140°. What is the degree measure of ∠BAD?


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Fixed. Thank you.
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Re: Triangles ABC and ADC are isosceles with AB = BC and AD = DC. Point D [#permalink] New post   03 Sep 2020, 05:40
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What is angle ABD here, can someone sketch it?
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Re: Triangles ABC and ADC are isosceles with AB = BC and AD = DC. Point D [#permalink] New post   08 Jan 2021, 23:09
IMO D.

70-20 = 50

See the attached image.
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Re: Triangles ABC and ADC are isosceles with AB = BC and AD = DC. Point D [#permalink] New post   16 Feb 2021, 00:11
Does the GMAT offer these styles of questions where you have to use your 'imagination' to figure out what the shape actually is? I burned 5 minutes trying to figure out what the actual figure looks like.
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Re: Triangles ABC and ADC are isosceles with AB = BC and AD = DC. Point D [#permalink] New post   03 May 2022, 21:33
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Re: Triangles ABC and ADC are isosceles with AB = BC and AD = DC. Point D [#permalink]
03 May 2022, 21:33
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