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505-555 (Easy)|   Geometry|            
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fozzzy
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In the figure above, DA ＝ DB ＝ DC, what is the value of x? Updated on: 01 Oct 2018, 01:34
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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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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In the figure above, DA ＝ DB ＝ DC, what is the value of x? 23 Jan 2013, 03:44
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fozzzy
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?
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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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In the figure above, DA ＝ DB ＝ DC, what is the value of x? 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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In the figure above, DA ＝ DB ＝ DC, what is the value of x? 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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In the figure above, DA ＝ DB ＝ DC, what is the value of x? 07 Aug 2023, 05:50
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