Question

which angles are congruent to each other?

Explanation:

Step1: Recall Congruent Angles Concepts

Congruent angles are angles that have the same measure. Vertical angles (opposite angles formed by two intersecting lines) are congruent. Alternate - interior angles (when a transversal crosses two parallel lines) are congruent.

Step2: Analyze Each Option

• For \(\angle10\) and \(\angle12\): These are adjacent angles, not vertical or alternate - interior angles. \(\angle10+\angle12 = 180^{\circ}\) (supplementary, not congruent).
• For \(\angle7\) and \(\angle4\): There is no property (vertical, alternate - interior, corresponding) that makes them congruent.
• For \(\angle11\) and \(\angle10\): These are adjacent angles, \(\angle11+\angle10=180^{\circ}\) (supplementary, not congruent).
• For \(\angle10\) and \(\angle6\): \(\angle10\) and \(\angle6\) are alternate - interior angles. If we assume the two non - vertical lines are parallel (implied by the angle - pair setup for such problems), by the Alternate - Interior Angles Theorem, \(\angle10\cong\angle6\).

Answer:

\(\angle10\) and \(\angle6\)