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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  In the figure above, if BC = CA, then y =

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Math Expert V
Joined: 02 Sep 2009
Posts: 55757
In the figure above, if BC = CA, then y =  [#permalink]

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Difficulty:   15% (low)

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

HideShow timer Statistics 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 774 times ]

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Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3368
Location: India
GPA: 3.12
Re: In the figure above, if BC = CA, then y =  [#permalink]

Show Tags 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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Intern  B
Joined: 13 Jul 2015
Posts: 19
Re: In the figure above, if BC = CA, then y =  [#permalink]

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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
Manager  B
Joined: 14 Sep 2016
Posts: 129
Re: In the figure above, if BC = CA, then y =  [#permalink]

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2 sides equal
so we get angle BAC = CBA = y

so, 2y + 30 =180
y = 75

Intern  B
Joined: 17 Apr 2017
Posts: 10
Location: India
Schools: NTU '20 (S)
GMAT 1: 720 Q48 V40 WE: Analyst (Consulting)
Re: In the figure above, if BC = CA, then y =  [#permalink]

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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
Manager  G
Joined: 27 Dec 2016
Posts: 232
Concentration: Marketing, Social Entrepreneurship
GPA: 3.65
WE: Marketing (Education)
Re: In the figure above, if BC = CA, then y =  [#permalink]

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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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There's an app for that - Steve Jobs. Re: In the figure above, if BC = CA, then y =   [#permalink] 19 Aug 2017, 21:59
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