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