Brent@GMATPrepNow wrote: ↑Sun May 03, 2020 5:37 am
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
Answer:
D
Source:
www.gmatprepnow.com
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
