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In the figure above, if PQRS is a parallelogram, then y - x =

(A) 30 (B) 35 (C) 40 (D) 70 (E) 100

In parallelogram corresponding angles are equal and consecutive angles are supplementary (supplementary angles are two angles that add up to 180°), thus:

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In the figure above, if PQRS is a parallelogram, then y - x =

(A) 30 (B) 35 (C) 40 (D) 70 (E) 100

In parallelogram corresponding angles are equal and consecutive angles are supplementary (supplementary angles are two angles that add up to 180°), thus:

In the figure above, if PQRS is a parallelogram, then y - x =

(A) 30 (B) 35 (C) 40 (D) 70 (E) 100

To solve we need to review some rules about parallelograms.

In parallelograms there are two main rules about the relationships between the angles:

1) Opposite angles are equal

Thus, angle P = angle R, and Angle Q = Angle S.

2) Consecutive angles are supplementary. That is, they add to 180 degrees.

Thus, angles Q and P add up to 180 degrees, as do angles P and S, angles S and R, and angles R and Q.

These rules can be used to solve the problem at hand.

We start by determining the value for angle P. We see that angle P is part of a straight angle. Since the exterior angle of angle P = 140 degrees, angle P must equal 40 degrees (since the two angles must sum to 180 degrees).

Using our first rule of parallelograms we see that angle R, which is equal to x, must also measure 40 degrees, since angles P and R are opposite angles.

Using our second rule of parallelograms, we know that angles R and S must add up to 180 degrees because they are consecutive angles. We note that angle S is equal to 2y. Thus:

2y + x = 180

2y + 40 = 180

2y = 140

y = 70

Therefore, the value of y – x is 70 – 40 = 30.

The answer is A.
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

In the figure above, if PQRS is a parallelogram, then y - x =

(A) 30 (B) 35 (C) 40 (D) 70 (E) 100

There are several ways to solve this question. Here's one approach;

Since the two highlighted angles below share the same line, they must add to 180°

So, ∠QPS = 40°

Next, since the PQ||RS, we know that the two circled angles are corresponding angles, which means those two angles are equal If 2y° = 140°, then we know that y = 70°

Finally, since the two angles (circled in blue below) are opposite angles in a parallelogram, we know that they are EQUAL. So, x = 40°