Data Sufficiency

VJesus12 wrote:

In the triangle ABC above, if AB = BC, find the value of y?

(1) x = 50
(2) z = 130

[spoiler]OA=D[/spoiler]

Source: Official Guide

From the figure, we see that /_BAC = xº (vertically opposite angle) and /_BCA = (180 - z)º (complementary angle)

Since AB = BC, the angles opposite to the side would also be equal.

Thus, /_BAC = /_BCA

x = 180 - z ---(1)

We have to get the value of yº.

In the ∆ABC, we have /_A + /_B + /_C = 180º

Thus, xº + yº + (180 - z)º = 180º

yº = zº - xº --- (2)

Let's take each statement one by one.

(1) x = 50

From (1) x = 180 - z, we have z = 180 - x

Plugging-in the value of z in eqn (2), we have y = 180 - x - x => y = 180 - 2x

y = 180 - 2*50 = 80º. Sufficient.

(2) z = 130

From (1) we have x = 180 - z

Plugging-in the value of x in eqn (2), we have y = z - 180 + z => y = 2z - 180

y = 2*130 - 180 = 260 - 180 = 80. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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