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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