Question

which angles are corresponding angles? ∠sru and ∠vur ∠sru and ∠tur ∠tuw and ∠qru ∠tur and ∠qru

Explanation:

Step1: Recall Corresponding Angles Definition

Corresponding angles are formed when a transversal intersects two parallel lines (or non - parallel lines, but the position is key). They are in the same relative position at each intersection.

Step2: Analyze Each Option

• For \(\angle SRU\) and \(\angle VUR\): These are alternate interior angles (if lines \(TV\) and \(QS\) are parallel), not corresponding.
• For \(\angle SRU\) and \(\angle TUR\): Let's check the positions. The transversal is \(WP\), and lines \(TV\) and \(QS\) are the two lines. \(\angle TUR\) is at the intersection of \(TV\) and \(WP\), \(\angle SRU\) is at the intersection of \(QS\) and \(WP\). Wait, no, let's re - check. Wait, the correct corresponding angles should be \(\angle TUR\) and \(\angle QRU\)? Wait, no, let's look at the last option: \(\angle TUR\) and \(\angle QRU\). Wait, no, let's re - examine the lines. The two lines are \(TV\) (with points \(T, U, V\)) and \(QS\) (with points \(Q, R, S\)), and the transversal is \(WP\) (with points \(W, U, R, P\)). Corresponding angles are in the same "corner" relative to the transversal and the two lines. \(\angle TUR\) is above line \(TV\) and to the left of transversal \(WP\), \(\angle QRU\) is above line \(QS\) and to the left of transversal \(WP\). Wait, no, let's check the option \(\angle TUR\) and \(\angle QRU\). Wait, maybe I made a mistake. Wait, the correct pair: Let's see the lines \(TV\) and \(QS\) are parallel (assuming from the diagram, as they are both going in the same direction). The transversal is \(WP\). Corresponding angles: \(\angle TUR\) (at \(U\), between \(TV\) and \(WP\)) and \(\angle QRU\) (at \(R\), between \(QS\) and \(WP\)) are in the same relative position (above the line, same side of transversal? Wait, no, let's check the other option. Wait, the option \(\angle TUR\) and \(\angle QRU\): Let's see, \(\angle TUR\) is formed by \(TV\) and \(WP\), \(\angle QRU\) is formed by \(QS\) and \(WP\). They are in the same corresponding position (both are above their respective lines and on the same side of the transversal). Wait, maybe the correct answer is \(\angle TUR\) and \(\angle QRU\). Wait, no, let's check the last option: \(\angle TUR\) and \(\angle QRU\). Wait, maybe I messed up the first analysis. Let's re - do:

Corresponding angles: When two lines are cut by a transversal, corresponding angles are in the same relative position. So, for lines \(TV\) and \(QS\) cut by transversal \(WP\), \(\angle TUR\) (at \(U\), between \(TV\) and \(WP\), upper left) and \(\angle QRU\) (at \(R\), between \(QS\) and \(WP\), upper left) are corresponding. The other options:

• \(\angle SRU\) and \(\angle VUR\): alternate interior.
• \(\angle SRU\) and \(\angle TUR\): not same position.
• \(\angle TUW\) and \(\angle QRU\): \(\angle TUW\) is a different angle (at \(U\), above \(TV\) and to the left of \(WP\) but \(\angle TUW\) is adjacent to \(\angle TUR\)). So the correct pair is \(\angle TUR\) and \(\angle QRU\).

Answer:

\(\angle TUR\) and \(\angle QRU\) (the last option: \(\boldsymbol{\angle TUR}\) and \(\boldsymbol{\angle QRU}\))