in triangle PQR , if PQ = x + 2 and PR = y, which of the angles of triangle PQR has the greatest degree measure?
1. y = x + 3
2. x = 2
1. y = x + 3
2. x = 2
On these types of questions, look to see if the triangle displays any of the "special" properties meaning it is isoceles or has sides that suggest 30/60/90 or equilateral, etc. This problem doesn't exhibit any special characteristics so you should assume you know nothing about the triangle.
Since you cannot make any assumptions about the triangle draw it super weird so you dont mistakenly interpret your own drawing and add hidden assumptions.
What info is given? Only the measure of two sides of the triangle - what triangle property deals with that? The only one I know of is the rule that the sum of any two sides of the triangle must be greater than the third side. In addition, we know that the largest angle in a triangle will be opposite the largest side so the question is: Which side has the longest length?
(1) y = x + 3
Now we know two sides: x + 3 and x + 2. But we do not know anything about the last side. It could anything in the range of 0.001 (repeating) to 2x + 4.9999999 (repeating) because none of these values would violate the rule. So this is INSUFFICIENT.
(2) x = 2
Given this information, we know one side PQ has a length of 4, but we have no info on PR and QR; they could be any values as long as they do not violate the rule. INSUFFICIENT.
(1+2) Together, from (1) we know the range of values for the last side fall within 0.0000001 to 2x + 4.99999 and from (2) we can determine a specific range: 0.00001 to 2(2) + 4.99999. We know that PQ = 2 + 2 = 4 and PR = y = x + 3 = 2 + 3 to 5. So two sides are 4 and 5, but we're still left with a range of values for the last side. INSUFFICIENT.
Is E the OA?
But later I realize it can be 2 also]. So for me OA is E.
