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# In the figure above, if BC = CD and angle ADC = 90 degrees, then what

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Math Expert
Joined: 02 Sep 2009
Posts: 52285
In the figure above, if BC = CD and angle ADC = 90 degrees, then what  [#permalink]

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03 Jan 2016, 12:32
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96% (01:19) correct 4% (00:00) wrong based on 75 sessions

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In the figure above, if BC = CD and angle ADC = 90 degrees, then what is the value of x?

A. 45
B. 50
C. 70
D. 75
E. 100

Attachment:

2016-01-04_0031.png [ 6.39 KiB | Viewed 1427 times ]

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Re: In the figure above, if BC = CD and angle ADC = 90 degrees, then what  [#permalink]

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03 Jan 2016, 19:30
1
[quote="Bunuel"]
In the figure above, if BC = CD and angle ADC = 90 degrees, then what is the value of x?

angle BDC also = 70
90-70=20
angle ABD=180-70=110

180-110-20
=50

B. 50
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Re: In the figure above, if BC = CD and angle ADC = 90 degrees, then what  [#permalink]

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03 Jan 2016, 23:29
Slightly longer method:

1. CBD = 70
2. Due to the isosceles triangle angle rules, BDC = 70
3. BCD = 180 - 70 - 70
4. BCD = 40
5. BAD (angle x) = 180 - 90 (due to right triangle) - 40
6. BAD (angle x) = 50

The answer is B, x = 50.
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Re: In the figure above, if BC = CD and angle ADC = 90 degrees, then what  [#permalink]

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04 Jan 2016, 04:41
Bunuel wrote:

In the figure above, if BC = CD and angle ADC = 90 degrees, then what is the value of x?

A. 45
B. 50
C. 70
D. 75
E. 100

Attachment:
2016-01-04_0031.png

BC=CD means angle CBD = CDB =70 and angle BCD=40. BCD+CDA+CAD=180 -> 40+90+x=180, hence x=50
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Re: In the figure above, if BC = CD and angle ADC = 90 degrees, then what  [#permalink]

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07 Mar 2017, 16:12
Bunuel wrote:

In the figure above, if BC = CD and angle ADC = 90 degrees, then what is the value of x?

A. 45
B. 50
C. 70
D. 75
E. 100

We can use triangle ABD to determine the value of x (since the angle with x degrees is angle A of triangle ABD). Let’s first determine the measures of the other two angles, angle ABD and angle BDA.

Using the given diagram, we see that angle ABD = 180 - 70 = 110 degrees.

Since BC = CD, angle CBD = angle CDB. Since angle CBD = 70 degrees, angle CDB = 70 degrees. Furthermore, angle BDA = 90 - 70 = 20 degrees.

Since we know the measures of the other two angles, x = angle A = 180 - 110 - 20 = 50 degrees.

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Re: In the figure above, if BC = CD and angle ADC = 90 degrees, then what &nbs [#permalink] 07 Mar 2017, 16:12
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