Question

1. choose the correct answer.

which are alternate interior angles?
∠4 and ∠5
∠7 and ∠2
∠6 and ∠4
∠2 and ∠5

Explanation:

Step1: Recall the definition of alternate interior angles

Alternate interior angles are non - adjacent angles that lie between two lines (here lines \(l\) and \(m\)) and on opposite sides of a transversal (here line \(t\)).

Step2: Analyze each option

• For \(\angle4\) and \(\angle5\):

They lie between lines \(l\) and \(m\) and on opposite sides of transversal \(t\).

• For \(\angle7\) and \(\angle2\):

\(\angle7\) is an exterior angle (below line \(m\)) and \(\angle2\) is an exterior angle (above line \(l\)) with respect to the region between \(l\) and \(m\).

• For \(\angle6\) and \(\angle4\):

They are on the same side of the transversal \(t\).

• For \(\angle2\) and \(\angle5\):

\(\angle2\) is above line \(l\) (exterior with respect to the region between \(l\) and \(m\)) and \(\angle5\) is between \(l\) and \(m\).

Answer:

\(\angle4\) and \(\angle5\)