Since vertically opposite angles are equal, we can conclude that y° = z°



If y° = z°, then we can take the angle y° (on the bottom right of the triangle) and replace it with z°



Since ∆ABC has two EQUAL angles, we know that it also has two EQUAL SIDES


Since vertically opposite angles are equal, we can conclude that the missing angle (shown below) is 2z°

At this point, the 3 angles are labeled, z°, z° and 2z°
Since angles in a triangle must add to 180°, we can write: z + z + 2z = 180
Simplify: 4z = 180
Solve, z = 45°
This also means 2z = 90°

When we add these 3 angles to our diagram . . .

. . . we see that we actually have a RIGHT TRIANGLE

ASIDE: The diagrams in GRE math questions are not necessarily drawn to scale. So, even though ∆ABC doesn't LOOK like a right triangle, it IS actually a right triangle.
In fact, we could actually redraw the triangle as follows:


At this point, it's easy to calculate the area of ∆ABC

Area = (base)(height)/2
= (1)(1)/2
= 1/2

Answer: E

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