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