The correct option is A only.
A) ∠RXZ and ∠YXZ
B) ∠PXQ and ∠RXS
C) ∠YZX and ∠UZT
D) ∠WZX and ∠XYZ
Supplementary angles are those angles whose measure add up to 180°.
Generally, Whenever the rays of two adjacent angles form a line then the two angles are Supplementary angles for each other, as in case 1.
A) ∠RXZ and ∠YXZ
These are supplementary angles because ∠RXZ and ∠YXZ form a straight line going through points R, X, Y and, V.
B) ∠PXQ and ∠RXS
These are not supplementary angles as ∠QXR is in between the two, therefore, the sum will not be 180°.
C) ∠YZX and ∠UZT
These are not supplementary angles because they are equally opposite angles.
D) ∠WZX and ∠XYZ
These are not supplementary angles, They are a part of a triangle, therefore, the sum will not be 180°.
Hence, the correct option is A only.
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