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In the figure above, DA = DB = DC, what is the value of x?

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In the figure above, DA = DB = DC, what is the value of x?  [#permalink]

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New post Updated on: 01 Oct 2018, 01:34
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In the figure above, DA = DB = DC, what is the value of x?

(A) 10
(B) 20
(C) 30
(D) 40
(E) 50


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Originally posted by fozzzy on 23 Jan 2013, 02:45.
Last edited by Bunuel on 01 Oct 2018, 01:34, edited 3 times in total.
Renamed the topic, edited the question and added the OA.
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Re: In the figure above, DA = DB = DC, what is the value of x?  [#permalink]

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New post 23 Jan 2013, 03:44
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fozzzy wrote:
In the figure above DA=DB=DC. What is the value of x?

a)10
b)20
c)30
d)40
e)50


do you approach this problem using property of isosceles triangle?


Yes. Property of isosceles triangle and the sum of the internal angles of a triangle.

50 + 50 + 30 + 30 + x + x = 180

x = 10
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Re: In the figure above, DA = DB = DC, what is the value of x?  [#permalink]

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New post 23 Jan 2013, 03:35
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Don't know about what others think but I shall approach this problem using the property of isosceles triangles.
The two equal sides will have the same measure in angles too.
Since DA=DC, hence angle DAC must be 50. Similarly, angle ABD must be 30. Thus, angle BDA=180-60 or 120 and angle ADC=180-100=80.
Angle BDC is 120+80=200.
Also, since DB=DC, hence angle DBC= angle DCB and angle BDC=360-200=160.
160+2x=180, therefore x=10.
Hope that helps.
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Re: In the figure above, DA = DB = DC, what is the value of x?  [#permalink]

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New post 24 Aug 2017, 23:51
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As DA = DB = DC, each of the triangle have 2 angles with the same magnitude.

Therefore,
In triangle DAC, Angle DAC = DCA = 50(the third angle is 180 -100 = 80)
In triangle BDA, Angle DAB = DBA = 30(the third angle is 180 - 60 = 120)

To determine the value of BDC,
We have a point D, and the sum of all the angles around it is 360
The third angle BDC = 360 - (80 + 120) = 160
In Triangle BDC, 160 + 2x = 180 => x = 10(Option A)
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Re: In the figure above, DA = DB = DC, what is the value of x? &nbs [#permalink] 24 Aug 2017, 23:51
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