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# In the figure above, AB = AC and CB = CD. What is x?

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Math Expert
Joined: 02 Sep 2009
Posts: 62290
In the figure above, AB = AC and CB = CD. What is x?  [#permalink]

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07 Feb 2020, 06:48
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Difficulty:

55% (hard)

Question Stats:

64% (01:41) correct 36% (02:07) wrong based on 45 sessions

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In the figure above, AB = AC and CB = CD. What is x?

A. 50
B. 80
C. 100
D. 130
E. 160

Attachment:

Triangles.JPG [ 7.81 KiB | Viewed 558 times ]

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Re: In the figure above, AB = AC and CB = CD. What is x?  [#permalink]

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07 Feb 2020, 07:05
1
Approach:

Given: AB = AC, outer angle on C = 160 deg

- So angle BCD = 80 deg

Further Given: CB = CD, So angle BDC and CBD be 50 deg each.

- So angle BDA or x = 180 - 50 = 130 deg

Option D!
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Re: In the figure above, AB = AC and CB = CD. What is x?  [#permalink]

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09 Feb 2020, 01:13
Bunuel wrote:

In the figure above, AB = AC and CB = CD. What is x?

A. 50
B. 80
C. 100
D. 130
E. 160

Attachment:
Triangles.JPG

A + 160 = 180
--> A = 20 deg

Since ABC is an isosceles triangle ∠ABC = ∠BCA = Y (assume)
--> A + B + C = 180
--> 2Y = 160
--> Y = 80 deg

Since triangle CBD is isosceles,
∠DBC = ∠BDC = Z
--> Z + Z + 80 = 180
--> 2Z = 100
--> Z = 50

At point D, X + Z = 180
--> X = 180 - 50 = 130 deg

Option D
Re: In the figure above, AB = AC and CB = CD. What is x?   [#permalink] 09 Feb 2020, 01:13
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