Question

Can anyone help me answer this Math question ?

Answer 1

The supplement of <S . . . Yes

the complement of <X . . . No   (the SUPPLEMENT of <X is)

the angle adjacent to <Z . . . Yes   (that's <Y)

angle corresponding to <R . . . Yes  (<T and <R are "vertical" angles)
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The angles equal to <T :

<R
supplement of <U
supplement of <S
<W
<Y
supplement of <Z
supplement of <X

Answer 2

The only false answer is "The complement of X"

Let's look at each alternative.

"The supplement of S": the supplement of an angle is what it's lacking to 180° (e.g. the supplement of 30° would be 150°). Since S + T creates an angle that starts and ends on the same line (the one which crosses line a and line b), (S+T) is an 180° angle (given that both aren't 0°). So T is the supplement of S and is, obviously, equal to T.

"The complement of X": the complement of an angle is what it's lacking to 90°. You can clearly see that X is an acute angle, smaller than 90°, and that T is an obtuse angle, bigger than 90°; it is, therefore, clear that what X lacks to get to 90° can't be equal to T, which is itself bigger than 90°.

"The angle adjacent to Z": both W and Y are adjacent to Z since they share a side, have the same vertex and do not overlap. Since a and b are parallel and there is a LINE crossing them, which means that it doesn't change direction, you know that X = S and T = Y.

"The angle corresponding to R": I guess you can figure this one by now. :)