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02 May 2020, 14:04
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D
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Difficulty:
35%
(medium)
Question Stats:
78% (02:42) correct
22%
(02:43)
wrong
based on 108
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If triangles PQR and LMN are equilateral triangles, what is the value of k in terms of x and y?
A) 60 + x – y
B) 120 – 2x + y
C) 120 – x + y
D) 180 – x – y
E) 180 – 2x + y
Updated on: 17 May 2021, 08:30
Originally posted by BrentGMATPrepNow on 02 May 2020, 22:32.
Last edited by BrentGMATPrepNow on 17 May 2021, 08:30, edited 2 times in total.
Last edited by BrentGMATPrepNow on 17 May 2021, 08:30, edited 2 times in total.
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BrentGMATPrepNow
First of all, since the two triangles are equilateral triangles, we know that all of the their angles are 60°
So we'll add this to our diagram (in a few key places)
Next, we'll focus on two angles, which I have labelled a and b
Since angles on a line add to 180°, we can write: x + 60 + a = 180
Subtract 60 from both sides: x + a = 120
Subtract x from both sides to get: a = 120 - x
When we apply the same logic to the other angles, we get: b = 120 - y
Add this to our diagram:
Now let's focus on the red triangle below.
Since angles in a triangle always add to 180°, we can write: w + (120 - x) + (120 - y) = 180
Simplify to get: w - x - y + 240 = 180
Subtract 240 from both sides: w - x - y = -60
Add x and add y to both sides of the equation to get: w = x + y - 60
Add this to our diagram to get:
Since opposite angles are always equal, we know that the opposite angle must also be x + y - 60
Finally, we can focus on the red triangle below.
Since angles in a triangle always add to 180°, we can write: k + 60 + (x + y - 60) = 180
Simplify: k + x + y = 180
Subtract x and subtract y from both sides to get: k = 180 - x - y
Answer: D
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General Discussion
02 May 2020, 15:19
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∠ORN = 180-60-x = 120-x
∠ONR = 120-y
∠RON = ∠SOQ = 180-(120-x)-(120-y) = x+y-60
∠SQO = 60
k = 180-60-(x+y-60) = 180-x-y
∠ONR = 120-y
∠RON = ∠SOQ = 180-(120-x)-(120-y) = x+y-60
∠SQO = 60
k = 180-60-(x+y-60) = 180-x-y
BrentGMATPrepNow
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