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(1) x = y. This implies that x = y = 90° (straight line is 180°, hence each must be 90°) --> y = a = 90° (straight line is 180°, hence each must be 90°). So, the question asks whether a = b = 90°. Rotation of the lower line changes the measure of angle b, so there is no way to determine whether it's 90°. Not sufficient.
(2) c = x. Clearly insufficient.
(1)+(2) Since from (2) c = x, then from (1) c = x = y = 90°. Now, if c = 90°, then b = 90° too. Therefore a = b = 90°. Sufficient.
(1) x = y. This implies that x = y = 90° (straight line is 180°, hence each must be 90°) --> y = a = 90° (straight line is 180°, hence each must be 90°). So, the question asks whether a = b = 90°. Rotation of the lower line changes the measure of angle b, so there is no way to determine whether it's 90°. Not sufficient.
(2) c = x. Clearly insufficient.
(1)+(2) Since from (2) c = x, then from (1) c = x = y = 90°. Now, if c = 90°, then b = 90° too. Therefore a = b = 90°. Sufficient.
(1) x = y. This implies that x = y = 90° (straight line is 180°, hence each must be 90°) --> y = a = 90° (straight line is 180°, hence each must be 90°). So, the question asks whether a = b = 90°. Rotation of the lower line changes the measure of angle b, so there is no way to determine whether it's 90°. Not sufficient.
(2) c = x. Clearly insufficient.
(1)+(2) Since from (2) c = x, then from (1) c = x = y = 90°. Now, if c = 90°, then b = 90° too. Therefore a = b = 90°. Sufficient.
(1) x = y. This implies that x = y = 90° (straight line is 180°, hence each must be 90°) --> y = a = 90° (straight line is 180°, hence each must be 90°). So, the question asks whether a = b = 90°. Rotation of the lower line changes the measure of angle b, so there is no way to determine whether it's 90°. Not sufficient.
(2) c = x. Clearly insufficient.
(1)+(2) Since from (2) c = x, then from (1) c = x = y = 90°. Now, if c = 90°, then b = 90° too. Therefore a = b = 90°. Sufficient.
(1) x = y. This implies that x = y = 90° (straight line is 180°, hence each must be 90°) --> y = a = 90° (straight line is 180°, hence each must be 90°). So, the question asks whether a = b = 90°. Rotation of the lower line changes the measure of angle b, so there is no way to determine whether it's 90°. Not sufficient.
(2) c = x. Clearly insufficient.
(1)+(2) Since from (2) c = x, then from (1) c = x = y = 90°. Now, if c = 90°, then b = 90° too. Therefore a = b = 90°. Sufficient.
One Q. If we consider only second statement i.e. c=x
This means, b= 180-x (straight lines, b+c=180)
Also, y= 180-x, this implies that a=x.
From here we can easily deduce that a and b are not equal.
Can you please tell me where exactly I have gone wrong ?
Thanks, Gaurav
Non-adjacent angles formed by the intersection of two straight lines are always equal, so a = x regardless whether c = x.
Also, I don't understand how you got that "we can easily deduce that a and b are not equal". Consider the simplest example to prove that a can be equal to b: a = b = c = x = y = 90 degrees.
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Statement 1: x = y To establish the comparison between angles a and b we need to establish the relation between one of the angles {x, y, a} and {b, c} First statement doesn't establish relationship between the two sets of angles. Hence, NOT SUFFICIENT
Statement 2: c = x Since, Angle x = Angle a [Vertically Opposite angles] and c = x therefore c = x = a but, c+b = 180 i.e. a + b = 180 but a and b may or may NOT be equal.Hence, NOT SUFFICIENT
Combining the two statements x = y = c = a = 90 degrees [because x+y = 180] and a + b = 180 i.e. b = 90 = a SUFFICIENT
Answer: option C
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50% (01:18) correct 
