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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
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In triangle ABC, AD = BD = DC (see figure). What is x?
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01 Mar 2021, 06:00
01 Mar 2021, 06:00
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84% (01:48) correct
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In triangle ABC, AD = BD = DC (see figure). What is x?
A. 4
B. 6
C. 8
D. 10
E. 12
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Re: In triangle ABC, AD = BD = DC (see figure). What is x?
[#permalink]
01 Mar 2021, 23:27
01 Mar 2021, 23:27
1
GeminiHeat wrote:
Attachment:
22.jpg
In triangle ABC, AD = BD = DC (see figure). What is x?
A. 4
B. 6
C. 8
D. 10
E. 12
Since, AD = BD = DC
We have 2 Isosceles triangles: BDC, BDA and 1 Equilateral triangle: ADC
In ADC: AD = DC
Angle DAC = Angle DCA = 60
So, Angle ADC = 60
Now, In BDC: BD = DC
Angle DCB = Angle DBC = 20
So, Angle BDC = 140
And, In BDA: BD = DA
Angle DBA = Angle DAB = x
Angle BDA = 360 - 140 - 60 = 160
i.e. 2x = 180 - 160 = 20
x = 10
Hence, option D
Re: In triangle ABC, AD = BD = DC (see figure). What is x?
[#permalink]
02 Mar 2021, 07:42
02 Mar 2021, 07:42
1
given
AD = BD = DC
so from △ADC ∠DAC=60
from △BDC ∠DBC=20
from △BDA ∠BAD=x
from △ABC ∠A=x+60
∠B=x+20
∠C=80
so ∠A+∠B+∠C=180
2x+160=180
x=10
option D is correct
AD = BD = DC
so from △ADC ∠DAC=60
from △BDC ∠DBC=20
from △BDA ∠BAD=x
from △ABC ∠A=x+60
∠B=x+20
∠C=80
so ∠A+∠B+∠C=180
2x+160=180
x=10
option D is correct
