What is the value of z? Image (NOTE: Figure not drawn to scale.) (1)

Using the fact that angles on opposite sides of an X are equal, and the fact that the angles in a triangle add to 180, then working through the diagram, in each triangle we find the angles are x, x and 180 - 2x. In particular, the angle at B is 180 - 2x, so if that angle is 90 degrees, then x must be 45 degrees, and Statement 2 is sufficient alone, while Statement 1 is not, and the answer is B.

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I'd caution that you should be careful applying logic like this in DS questions. It's true that when two statements are exactly equivalent (when they provide identical information) then the answer can never be C, because then you'd never learn anything new by combining the Statements; the answer can only be D or E in that case. But the two Statements here are not equivalent: Statement 2 gives you more information than Statement 1.

In theory, you can learn how to rule out some DS answers because of logical relationships like this -- when two Statements are equivalent, the answer must be D or E, or when Statement 2 is a specific case of Statement 1 (as happens here), the answer can only be B, D or E (since if we can solve in the general case, we definitely can in the specific case, but sometimes we can solve in the specific case but not in the general one, and combining the statements never give us new information). In practice, however, this kind of logic is rarely helpful on actual GMAT questions, which is easy to confirm just by going through a batch of authentic high-level problems, asking how often you can readily tell that two Statements give identical information, or how often one Statement is clearly a special case of the other. I've seen some prep books that devote a lot of space to DS Statement logic issues like this, but I don't think it makes any difference to learn about it, especially since it can be time-consuming and confusing to think through properly in questions like this one.

If you plot the figure and write down the values of all the angles in terms of z (only using the data provided in the stem) you can see that angle B comes out to be (180 - 2z)°

Statement 2 gives us that angle B is 90° which means 180-2z=90 or that 2z=90 or z=45 which helps us determine a unique value for z.

Hence, we cannot say that Statement 2 doesn't provide us any additional information. In fact, using statement 2 alone we can answer the question and hence, correct answer should be B, not E.

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Thank you for pointing out my error! Bellow I have attached an image correcting my initial and interpreting the information with less words so it might be easier to follow .

==> B is the correct answer!

Please refer to the attached fig. below:
Even without the statements we can see that \(\angle B = 180 -2z\)

(1) Angle A is an acute angle.

This means z is less than 90. However we still do not know the exact value of z . INSUFF.

(2) Angle B is a right angle.

which means \(180 -2z= 90\)

\(2z=90\)

\(z=45\)

SUFF.

Ans B