which pair of angles is supplementary?\n∠rxz and ∠yxz\n∠pxq and ∠rxs\n∠yzx and ∠uzt\n∠wzx and ∠xyz
which pair of angles is supplementary?\n∠rxz and ∠yxz\n∠pxq and ∠rxs\n∠yzx and ∠uzt\n∠wzx and ∠xyz
Answer
Explanation:
Step1: Recall the definition of supplementary angles
Supplementary angles are two angles whose sum is (180^{\circ}).
Step2: Analyze (\angle RXZ) and (\angle YXZ)
Since (PS\parallel WT) and (RY) is a transversal, (\angle RXZ) and (\angle YXZ) are same - side interior angles. By the same - side interior angles theorem, if two parallel lines are cut by a transversal, then the sum of same - side interior angles is (180^{\circ}).
Step3: Analyze (\angle PXQ) and (\angle RXS)
(\angle PXQ) and (\angle RXS) are vertical angles (not supplementary, vertical angles are equal).
Step4: Analyze (\angle YZX) and (\angle UZT)
(\angle YZX) and (\angle UZT) are vertical angles (not supplementary, vertical angles are equal).
Step5: Analyze (\angle WZX) and (\angle XYZ)
There is no relation (such as same - side interior, linear pair etc.) that would make their sum (180^{\circ}).
Answer:
(\angle RXZ) and (\angle YXZ)