SAT Math Multiple Choice Practice Question 70: Answer and Explanation
What is the value in degrees of a in this diagram?
Correct Answer: D
D. Look first at the large triangle. You know one angle, 38°, and the other two angles are both equal to p + q. Thus, you can write (p + q) + (p + q) + 38 = 180, which gives you 2p + 2q + 38 = 180, and, finally, 2p + 2q = 142. At this point, some people frustrate themselves by trying to figure out what p and q equal. Unfortunately, you don't have enough information to do that calculation; however, if 2p + 2q = 142, you can divide both sides by 2 to get p + q = 71. If you look at the little triangle, you realize that you now have all the information you need. Because the angles of the little triangle are a, p, and q, you can write a + p + q = 180; because p + q = 71, a + 71 = 180, and a = 109.