Question

1. choose the correct answer.

which are same - side exterior angles?
∠1 and ∠7
∠3 and ∠5
∠3 and ∠7
∠1 and ∠6

Explanation:

Step1: Recall the definition of same - side exterior angles

Same - side exterior angles are two angles that are on the same side of the transversal and outside the two lines.

Step2: Analyze each option

• For \(\angle1\) and \(\angle7\):
• \(\angle1\) is above line \(l\) and \(\angle7\) is below line \(m\). They are not on the same side of the transversal \(t\).
• For \(\angle3\) and \(\angle5\):
• \(\angle3\) is between line \(l\) and transversal \(t\), \(\angle5\) is between line \(m\) and transversal \(t\). They are interior angles.
• For \(\angle3\) and \(\angle7\):
• \(\angle3\) is between line \(l\) and transversal \(t\), \(\angle7\) is below line \(m\). \(\angle3\) is an interior angle and \(\angle7\) is an exterior angle.
• For \(\angle1\) and \(\angle6\):
• \(\angle1\) is above line \(l\) (exterior to the region between \(l\) and \(m\)), \(\angle6\) is above line \(m\) (exterior to the region between \(l\) and \(m\)). And they are on the same side of the transversal \(t\).

Answer:

\(\angle1\) and \(\angle6\)