In Case I， x is greater than 45 degrees; in Case II， x equals 45 degrees; in　Case III， x is less than 45 degrees. Hence， the given information is not sufficient to answer the question.

　　Example 2： Three rays emanate from a common point and form three angles with　measures p， q， and r. What is the measure of q + r ?

　　It is natural to make the drawing symmetric as follows：

　　In this case， p = q = r = 120， so q + r = 240. However， there are other drawings possible. For example：

　　In this case， q + r = 180. Hence， the given information is not sufficient to　answer the question.

　　Problems：

　　1. Suppose 3p + 4q = 11. Then what is the value of q?

　　 p is prime.

　　 q = -2p

　　 is insufficient. For example， if p = 3 and q = 1/2， then 3p + 4q = 3

　　+ 4 = 11. However， if p = 5 and q = -1， then 3p + 4q = 3 + 4 = 1

　　1. Since the value of q is not unique， is insufficient.

　　Turning to ， we now have a system of two equations in two unknowns. Hence， the system can be solved to determine the value of q. Thus， is suffici　　

　　2. What is the perimeter of triangle ABC above?

　　 The ratio of DE to BF is 1： 3.

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