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# In the figure above, if BC = CA, then y =

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Joined: 02 Sep 2009
Posts: 64068
In the figure above, if BC = CA, then y =  [#permalink]

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17 Aug 2017, 22:50
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15% (low)

Question Stats:

97% (00:40) correct 3% (00:41) wrong based on 53 sessions

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In the figure above, if BC = CA, then y =

(A) 15
(B) 60
(C) 75
(D) 150
(E) 165

Attachment:

2017-08-18_1028_002.png [ 7.2 KiB | Viewed 887 times ]

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Re: In the figure above, if BC = CA, then y =  [#permalink]

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17 Aug 2017, 23:23

In the figure above, if BC = CA, then Angle CBA = BAC = y
Also since the lines intersect at C, Angle BCA = CDE = 30

In a triangle, the sum of the three angles equals 180
2y + 30 = 180
2y = 150
Therefore, y = 75(Option C)
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Re: In the figure above, if BC = CA, then y =  [#permalink]

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18 Aug 2017, 01:01
Ans- C

BC= CA
Thus angle A=angle B (Angles oppsite to congruent sides)

BCA=DCE = 30 (vertically opposite angles).

In triangle BAC ,

Angle BCA+ Angle B+ Angle A = 180

30 +2x = 180 . Thus x = 75
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Re: In the figure above, if BC = CA, then y =  [#permalink]

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18 Aug 2017, 01:51
2 sides equal
so we get angle BAC = CBA = y

so, 2y + 30 =180
y = 75

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Re: In the figure above, if BC = CA, then y =  [#permalink]

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19 Aug 2017, 02:15
In the above figure,

Given that :
1. BC=CA so, angle CBA=CAB=y
2. Angle DCE=Angle BCA = 30 (since they both are vertical angles and will be equal)

There fore In Triangle ABC,
Angles (CBA + CAB + ACB) =180
y+y+30=180
So, y = 75
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Re: In the figure above, if BC = CA, then y =  [#permalink]

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19 Aug 2017, 20:59
Bunuel wrote:

In the figure above, if BC = CA, then y =

(A) 15
(B) 60
(C) 75
(D) 150
(E) 165

Attachment:
2017-08-18_1028_002.png

1. Since angle DCA = 30, angle BCA must be 30 (opposite angle is equal).
2. Look in the triangle ABC = angle CAB + angle ABC + angle BCA = 180. So, angle CAB + Angle ABC must be 150.
3. Since BC = CA, angle in front of this line must be equal. So, we divide 150 by 2 = 75 degree.

C.
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Re: In the figure above, if BC = CA, then y =   [#permalink] 19 Aug 2017, 20:59