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If AB=AC, BD=BC, and BD is the bisector of ∠ABC, then what is x?

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If AB=AC, BD=BC, and BD is the bisector of ∠ABC, then what is x?  [#permalink]

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New post 08 Sep 2016, 04:21
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If AB=AC, BD=BC, and BD is the bisector of ∠ABC, then what is x?

A. 27
B. 30
C. 32
D. 36
E. 42

Attachment:
T6000.png
T6000.png [ 6.44 KiB | Viewed 4517 times ]

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Re: If AB=AC, BD=BC, and BD is the bisector of ∠ABC, then what is x?  [#permalink]

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New post 09 Sep 2016, 07:41
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Bunuel wrote:
Image
If AB=AC, BD=BC, and BD is the bisector of ∠ABC, then what is x?

A. 27
B. 30
C. 32
D. 36
E. 42

Attachment:
T6000.png


Since, BD is the bisector of ∠ABC, we know that the other angle must be x....
Image

We're also told that AB=AC, which we can add to the diagram...
Image

Those two equal sides mean that the two highlighted angles (below) are equal
Image

So, the angle at vertex C must also be 2x....
Image

At this point, let's focus our attention on the blue triangle below...
Image

Since the blue triangle is an isosceles triangle, the 3rd angle must equal 2x....
Image

Since the angles in a triangle must add to 180 degrees, we can write: x + 2x + 2x = 180
Simplify: 5x = 180
Solve: x = 36

Answer:

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Re: If AB=AC, BD=BC, and BD is the bisector of ∠ABC, then what is x?  [#permalink]

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New post 08 Sep 2016, 05:35
In BDC,
∠BDC + ∠BCD + ∠DBC = 180 -----(1)

Since in ABC AB = AC, ∠ABC = ∠ACB
And IN BDC, BD=BC, ∠BDC = ∠BCD

Subst these facts in st. (1)

x + 2x + 2x = 180
x=36

Option D
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If AB=AC, BD=BC, and BD is the bisector of ∠ABC, then what is x?  [#permalink]

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New post 08 Sep 2016, 19:53
from given angle b = angle C and angle C = angle D

lets take angle b = K

the small triangle BDC = 180 degree

K is cut into half

K/2+K+K = 180

since angle B = angle C = angle D

K/2 which is x = 36
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Re: If AB=AC, BD=BC, and BD is the bisector of ∠ABC, then what is x?  [#permalink]

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New post 08 Sep 2016, 20:12
Angle a + 2x + 2x = 180, we know that x = a.

so: 2x + 2x + x = 180

5x = 180

x = 36
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Re: If AB=AC, BD=BC, and BD is the bisector of ∠ABC, then what is x?  [#permalink]

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New post 13 May 2018, 08:51
Bunuel wrote:
Image
If AB=AC, BD=BC, and BD is the bisector of ∠ABC, then what is x?

A. 27
B. 30
C. 32
D. 36
E. 42

Attachment:
The attachment T6000.png is no longer available


Please refer the picture :
1. As BD bisects ∠ABC, hence ∠ABD=∠DBC=x
2. As AB=AC, ∠ABC =2x=∠ACB
3. As BC=BD, ∠BCD=∠BCA=2x=∠BDC

Now in triangle BDC : ∠BCD+∠BDC+∠DBC = 2x+2x+x= 180 =====>x=36 ..... Hence I would go for option D.
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Re: If AB=AC, BD=BC, and BD is the bisector of ∠ABC, then what is x? &nbs [#permalink] 13 May 2018, 08:51
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