In the figure above, RST is a triangle with angle measures

Hi All,

We're told that In the figure above, RST is a triangle with angle measures as shown and PRTQ is a line segment. We're asked for the value of (X+Y). This question is built around a couple of Geometry lines involving Triangles and Lines. To start, the angles in the triangle (re: s, r and t) total 180 degrees and so do the pairs of angles (x+r) = 180 and (t+y) = 180.

(1) s = 40

With angle s, we know that r+t must total 140 degrees. Those two angles are part of the two 180 degree totals on the line, meaning that r+t+x+y = 360 degrees. We now know that r+t = 180, so....
r+t+x+y = 360
180+x+y = 360
x+y = 180
Fact 1 is SUFFICIENT

(2) r = 70

Fact 2 helps us to determine the value of angle x (since x+r = 180, we know that x = 110 degrees), but we don't know the value of y.
Fact 2 is INSUFFICIENT

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

AbeNeedsAnswers wrote: ↑

Sun May 05, 2019 9:15 pm

In the figure above, RST is a triangle with angle measures as shown and PRTQ is a line segment. What is the value of x + y ?

(1) s = 40
(2) r = 70

A

Source: Official Guide 2020

Given: RST is a triangle with angle measures as shown and PRTQ is a line segment

Target question: What is the value of x + y ?

Statement 1: s = 40
Since angles in a triangle add to 180°, we know that r° + t° = 140°
Since angles on a line add to 180°, we know that x° + r° = 180°, and we know that t° + y° = 180°
So, we can write: x° + r° + t° + y° = 180° + 180°
Rearrange: x° + y° + r° + t° = 360°
Substitute to get: x° + y° + 140° = 360°
Subtract 140° from both sides to get: x° + y° = 220°
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: r = 70
This tells us that x° = 110°, however we have no information about the value of any other angle.
Statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent