Question

which angles are supplementary angles? (image of intersecting lines with angles ∠tus, ∠wxu, ∠vux, ∠yxz, ∠tux) options: ∠tus and ∠wxu; ∠tus and ∠vux; ∠tus and ∠yxz; ∠tus and ∠tux

Explanation:

Step1: Recall Supplementary Angles

Supplementary angles are two angles whose sum is \(180^\circ\) (a straight angle). They can be adjacent (forming a linear pair) or non - adjacent.

Step2: Analyze Each Option

• Option 1: \(\angle TUS\) and \(\angle WXU\)

Since \(TV\parallel WY\) (from the diagram, as they are parallel lines cut by a transversal \(SZ\)), \(\angle TUS\) and \(\angle WXU\) are corresponding angles. Corresponding angles are equal when lines are parallel, so they are not supplementary (unless each is \(90^\circ\), which is not indicated here).

• Option 2: \(\angle TUS\) and \(\angle VUX\)

\(\angle TUS\) and \(\angle VUX\) are vertical angles. Vertical angles are equal, so they are not supplementary (unless each is \(90^\circ\), which is not indicated here).

• Option 3: \(\angle TUS\) and \(\angle YXZ\)

\(\angle YXZ\) and \(\angle WXU\) are vertical angles, and \(\angle TUS\) and \(\angle WXU\) are corresponding angles (so \(\angle TUS=\angle WXU\) and \(\angle YXZ = \angle WXU\), thus \(\angle TUS=\angle YXZ\)). So they are equal, not supplementary.

• Option 4: \(\angle TUS\) and \(\angle TUX\)

\(\angle TUS\) and \(\angle TUX\) form a linear pair. A linear pair of angles is supplementary because they lie on a straight line, so their sum is \(180^\circ\).

Answer:

\(\boldsymbol{\angle TUS}\) and \(\boldsymbol{\angle TUX}\)