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19 Dec 2019, 02:19
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In the figure given, what is the value of y?
(1) x = z
(2) a||b
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19 Dec 2019, 09:34
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Statement 1- If x=z, 2 lines crossing line a and line b are parallel
hence, y=180-43= 137 (corresponding angles)
Sufficient
Statement 2-
If a||b, x=43 and y= 180-z
Insufficient
hence, y=180-43= 137 (corresponding angles)
Sufficient
Statement 2-
If a||b, x=43 and y= 180-z
Insufficient
Bunuel
28 May 2023, 03:09
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This one's tricky because the image could be misleading. In approaching this question we need to be careful not to make any assumptions.
In the figure given, what is the value of y?
If x° = z°, then the two diagonal lines are parallel. Since they are parallel, we can then deduce y° using the interior angles property (sorry I'm not sure how to attach images here).
43° + y° = 180°
y° = 180° - 43° = 137°
Hence, statement 1 is sufficient.
It's tempting to deduce that statement 2 is sufficient but it's not. We can deduce the supplementary angle next to x° and subsequently x° using the interior angles property (43° + angle supplementary to x° = 180°; the angle supplementary to x° = 137°; x = 180°- 137° = 43°), but the fact that lines a and b are parallel tells us nothing about y° and z° other than the fact that y°+z°=180°.
In fact, because we don't know anything about the diagonal line on the right-hand side, the shape formed may as well be a trapezoid upside down.
I'd greatly appreciate it if you could confirm, Bunuel. Many thanks!
In the figure given, what is the value of y?
Quote:
If x° = z°, then the two diagonal lines are parallel. Since they are parallel, we can then deduce y° using the interior angles property (sorry I'm not sure how to attach images here).
43° + y° = 180°
y° = 180° - 43° = 137°
Hence, statement 1 is sufficient.
Quote:
It's tempting to deduce that statement 2 is sufficient but it's not. We can deduce the supplementary angle next to x° and subsequently x° using the interior angles property (43° + angle supplementary to x° = 180°; the angle supplementary to x° = 137°; x = 180°- 137° = 43°), but the fact that lines a and b are parallel tells us nothing about y° and z° other than the fact that y°+z°=180°.
In fact, because we don't know anything about the diagonal line on the right-hand side, the shape formed may as well be a trapezoid upside down.
I'd greatly appreciate it if you could confirm, Bunuel. Many thanks!
