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In triangle ABC, AD = BD = DC (see figure). What is x?

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GeminiHeat
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In triangle ABC, AD = BD = DC (see figure). What is x? [#permalink] New post   01 Mar 2021, 06:00
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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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D
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Re: In triangle ABC, AD = BD = DC (see figure). What is x? [#permalink] New post   01 Mar 2021, 23:27
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GeminiHeat wrote:
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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


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
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Re: In triangle ABC, AD = BD = DC (see figure). What is x? [#permalink] New post   02 Mar 2021, 07:42
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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
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Re: In triangle ABC, AD = BD = DC (see figure). What is x? [#permalink]
02 Mar 2021, 07:42
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