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# In the figure above DA=DB=DC. What is the value of x? a)10

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In the figure above DA=DB=DC. What is the value of x? a)10 [#permalink]  23 Jan 2013, 01:45
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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

do you approach this problem using property of isosceles triangle?
[Reveal] Spoiler: OA

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Re: In the figure above DA=DB=DC. What is the value of x? a)10 [#permalink]  23 Jan 2013, 02:44
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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? a)10 [#permalink]  23 Jan 2013, 02:35
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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? a)10 [#permalink]  04 Mar 2014, 17:36
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Re: In the figure above DA=DB=DC. What is the value of x? a)10   [#permalink] 04 Mar 2014, 17:36
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