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Re: If three straight lines intersect at a point as shown in the figure ab
[#permalink]
26 Apr 2019, 11:36
The Precise approach to this question will use the given information to find the specific numbers. We would rarely need to do this in DS questions, but this question provides a lot of information to start with: since two opposite angles between intersecting lines are equal, and since the sum of angles in a full circle is 360, we know that x+y+z+x+y+z=360, so 2x+2y+2z=360. Statement (1): if x=y=z, then (using 2x+2y+2z=360) we get 2x+2x+2x=360 >>> 6x=360 >>> x=60. Since statement (1) is enough on its own, answer choices (B), (C) and (E) are eliminated. Statement (2): If z=60, then (using 2x+2y+2z=360) we get 2x+2y+120=360. This is an equation with two variables, and thus not enough to find the exact value of x. Answer choice (D) is eliminated.
Since opposite angles are equal, we can add a few more things to our diagram to get:
Statement 1: x = y = z Since angles on a line add to 180°, we can see that the along the blue line must add to 180°
So, x + y + z = 180 If all three angles are equal, then x = y = z = 60 The answer to the target question is x = 60 Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: z = 60 Let's add this information to the diagram to get:
Notice that, if we rotate the green line, the value of x changes (for more on this strategy, see the second video below). Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
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