Question

Lines P S and W T are horizontal and parallel. Lines V R and Q R are diagonal and intersect lines P S and W T to form triangle X Y Z.

Which pair of angles is supplementary?


∠RXZ and ∠YXZ

∠PXQ and ∠RXS

∠YZX and ∠UZT

∠WZX and ∠XYZ

Answer 1

*see attachment below for the diagram being referred to

Answer:

∠RXZ and ∠YXZ

Explanation:

Supplementary angles are angles whose sum gives us 180°.

Let's consider each pair of angles given as options and see which of them are supplementary angles considering the given diagram:

Option 1: ∠RXZ and ∠YXZ.

∠RXZ and ∠YXZ are angles on a straight line, and they form a linear. A linear pair = 180°. Therefore, ∠RXZ and ∠YXZ pair is supplementary.

Option 2: ∠PXQ and ∠RXS do not form a linear pair, neither are they angles in a straight line, therefore, the angle pair ∠PXQ and ∠RXS, is not supplementary.

Option 3: ∠YZX and ∠UZT.

∠YZX and ∠UZT are vertical angles. Therefore, the angle pair ∠YZX and ∠UZT is not supplementary.

Option 4: ∠WZX and ∠XYZ.

There's no special relationship between ∠WZX and ∠XYZ, other than being angles of ∆XYZ. Therefore, the angle pair ∠WZX and ∠XYZ, is not supplementary.