Question

1. choose the correct answer.

which are same - side interior angles?
∠6 and ∠5
∠3 and ∠2
∠2 and ∠5
∠3 and ∠5

Explanation:

Step1: Recall the definition of same - side interior angles

Same - side interior angles are two angles that lie between two lines (in this case, lines \(l\) and \(m\)) and on the same side of a transversal (line \(r\)).

Step2: Analyze each option

• For \(\angle6\) and \(\angle5\): These are adjacent angles (they form a linear pair), not same - side interior angles.
• For \(\angle3\) and \(\angle2\): These are vertical angles (opposite angles formed by the intersection of two lines), not same - side interior angles.
• For \(\angle2\) and \(\angle5\): \(\angle2\) is above line \(l\) and \(\angle5\) is below line \(m\) (not between the two lines \(l\) and \(m\) with respect to the transversal \(r\)), so they are not same - side interior angles.
• For \(\angle3\) and \(\angle5\): \(\angle3\) and \(\angle5\) lie between lines \(l\) and \(m\) and on the same side of the transversal \(r\).

Answer:

\(\angle3\) and \(\angle5\) (the fourth option)