# SAT Math Multiple Choice Practice Question 414: Answer and Explanation

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**Question: 414**

**18.**

In rectangle *PQRS* above, what is *a + b* in terms of *x* ?

A. 90 + *x*

B. 90 – *x*

C. 180 + *x*

D. 270 – *x*

E. 360 – *x*

**Correct Answer:** A

**Explanation:**

**A** This is a great opportunity to plug in. Make up a value for *x*—let's say 40. Then name the two other angles created by the lines that meet at vertex *P*— let's call the one to the left of *x* (within the same triangle as the angle labeled *a*°) angle *y* and the one to the right of *x* (within the same triangle as the angle labeled *b*°) angle *z*. Now make up values for these two angles so the sum of *x, y,* and *z* is 90. Let's say that *y* = 30 and *z* = 20. Because both of these triangles are right triangles, *a* = 180 – 90 – 30 = 60, and *b* = 180 – 90 – 20 = 70. Thus *a* + *b* = 130, which becomes our target. Only A yields this answer.