Question

which angles are alternate exterior angles?
image of intersecting lines with points o, q, r, p, s, t, u, v and angle options: ∠rqt and ∠utq; ∠stv and ∠rqo; ∠utv and ∠stq; ∠utq and ∠rqo

Explanation:

Step1: Recall Alternate Exterior Angles Definition

Alternate exterior angles are formed when a transversal crosses two parallel lines. They lie outside the two lines and on opposite sides of the transversal.

Step2: Analyze Each Option

• Option 1: $\angle RQT$ and $\angle UTQ$: $\angle RQT$ is inside the lines, $\angle UTQ$ is inside too. Not exterior.
• Option 2: $\angle STV$ and $\angle RQO$: $\angle STV$ is outside the two lines (below line $SU$) and $\angle RQO$ is outside (above line $PR$), on opposite sides of transversal $OV$. Check positions: transversal $OV$, lines $PR \parallel SU$. $\angle STV$ (exterior, left of transversal) and $\angle RQO$ (exterior, right of transversal) – alternate exterior.
• Option 3: $\angle UTV$ and $\angle STQ$: Both are adjacent or interior. Not exterior.
• Option 4: $\angle UTQ$ and $\angle RQO$: $\angle UTQ$ is interior, $\angle RQO$ is exterior. Not both exterior.

Answer:

$\angle STV$ and $\angle RQO$ (the second option: $\boldsymbol{\angle STV}$ and $\boldsymbol{\angle RQO}$)