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In the figure below, what is the value of x?

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Bunuel
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In the figure below, what is the value of x? [#permalink] New post   23 Jun 2021, 01:30
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In the figure below, what is the value of x?

A. 60°
B. 75°
C. 90°
D. 105°
E. 135°



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C
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rajatchopra1994
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Re: In the figure below, what is the value of x? [#permalink] New post   23 Jun 2021, 02:43
Explanation:

Triangle ADC and BDC are isosceles triangles and AD=DC=DB.
Angle DCB = (180 - 90)/2 = 45 Deg = Angle DCA
Angle X = 180 - 45 - 45 = 90

IMO-C
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Re: In the figure below, what is the value of x? [#permalink] New post   23 Jun 2021, 03:21
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Triangle ACD and BCD are right angles isosceles triangle
Answer is C


Bunuel wrote:

In the figure below, what is the value of x?

A. 60°
B. 75°
C. 90°
D. 105°
E. 135°



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Re: In the figure below, what is the value of x? [#permalink] New post   23 Jun 2021, 03:39
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Given in the above figure,
DA = CD = DB
Also given angle CDA and CDB = 90
Which implies by triangle sum property , DBC = DCB = DCA = DAC (45)

x = 180 - ( 45 + 45)
=90

IMO C
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Re: In the figure below, what is the value of x? [#permalink] New post   23 Jun 2021, 13:48
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Bunuel wrote:

In the figure below, what is the value of x?

A. 60°
B. 75°
C. 90°
D. 105°
E. 135°



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∠DCA = ∠DCB = 45
∠DCA + ∠DCB + x = 180
90 + x = 180
x = 90 IMO, (C)!
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In the figure below, what is the value of x? [#permalink] New post   23 Jun 2021, 22:49
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[quote="Bunuel"]
In the figure below, what is the value of x?

A. 60°
B. 75°
C. 90°
D. 105°
E. 135°

IMO C, 90

As both the triangles ADC, BDC are right isosceles, Hence angle made by them is 45°.

Which make the whole triangle ABC another right isosceles triangle.Hence x=90°

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In the figure below, what is the value of x? [#permalink]
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