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In the figure above (OG16)

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boomgoesthegmat Senior | Next Rank: 100 Posts Default Avatar
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In the figure above (OG16)

Post Thu May 19, 2016 3:48 pm
ttp://postimg.org/image/5t37yr5oh/" target="_blank">

In the figure above, if z = 50, then x+ y =

A) 230
B) 250
C) 260
D) 270
E) 290

OA: D

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OptimusPrep Master | Next Rank: 500 Posts
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Post Thu May 19, 2016 8:07 pm
boomgoesthegmat wrote:
ttp://postimg.org/image/5t37yr5oh/" target="_blank">

In the figure above, if z = 50, then x+ y =

A) 230
B) 250
C) 260
D) 270
E) 290

OA: D
Since we need to find the value of x + y, we can solve the question intelligently to save some time.

In the smaller triangle, angles are 180 - y, 90 and 180 - x
180 - y + 90 + 180 - x = 180
x + y = 270

Correct Option: D

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Post Thu May 19, 2016 4:59 pm
Hi boomgoesthegmat,

This question requires an understanding of similar triangles, "line" rules (specifically that the angles on a line sum to 180 degrees) and that the angles in a triangle sum to 180 degrees.

We're told that Z=50. Since the two triangles have the same angles (they both have a 90 and the same angle "next" to angle X), we know that the triangles are similar. This means that Z and the angle "next" to Y are the SAME (meaning that they BOTH = 50).

By extension, Y + 50 = 180, so Y = 130.

The angles in the smaller triangle are 90, 50 and the missing angle. 90+50 = 140, so the missing angle = 40.

40 + X = 180, so X = 140

Thus, X+Y = 130+140 = 270

Final Answer: D

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