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# In the figure above, DA = DB = DC. What is the value of x?

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Math Expert
Joined: 02 Sep 2009
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Kudos [?]: 129059 [1], given: 12189

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

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24 Aug 2017, 23:37
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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

[Reveal] Spoiler:
Attachment:

2017-08-24_1251_003.png [ 9.94 KiB | Viewed 235 times ]
[Reveal] Spoiler: OA

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Kudos [?]: 129059 [1], given: 12189

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Kudos [?]: 596 [1], given: 16

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

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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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Kudos [?]: 596 [1], given: 16

Re: In the figure above, DA = DB = DC. What is the value of x?   [#permalink] 24 Aug 2017, 23:51
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