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

so, 2y + 30 =180
y = 75

answer = C
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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
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Bunuel

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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