Question

which of these are a pair of same side interior angles?

1. a) ∠3, ∠7

b) ∠6, ∠7
c) ∠3, ∠7
d) ∠2, ∠7
e) none of these

Explanation:

Step1: Recall Same-Side Interior Angles

Same - side interior angles are two angles that lie between two lines (the "interior") and on the same side of a transversal. The two lines are usually parallel, and the transversal cuts through them. The sum of same - side interior angles is \(180^{\circ}\) (supplementary) when the two lines are parallel.

Step2: Analyze Each Option

• Option A: \(\angle1\) and \(\angle7\) - \(\angle1\) and \(\angle7\) are not same - side interior angles. \(\angle1\) and \(\angle7\) are related as alternate exterior or other types of angles, not same - side interior.
• Option B: \(\angle6\) and \(\angle7\) - Let's consider the lines. If we assume the two non - transversal lines and the transversal, \(\angle6\) and \(\angle7\) lie between the two lines (interior) and on the same side of the transversal. Let's check the positions. The two lines cut by the transversal: \(\angle6\) and \(\angle7\) are between the two lines (the ones with the angles numbered 1 - 2 - 7 - 8 and 3 - 4 - 5 - 6) and on the same side of the transversal (the line that intersects these two lines). So \(\angle6\) and \(\angle7\) satisfy the definition of same - side interior angles.
• Option C: \(\angle3\) and \(\angle7\) - \(\angle3\) and \(\angle7\) do not lie between the two lines (interior) on the same side of the transversal. Their positions do not match the definition of same - side interior angles.
• Option D: \(\angle2\) and \(\angle7\) - \(\angle2\) and \(\angle7\) are adjacent angles (they form a linear pair? No, but their positions do not match the same - side interior angle definition. They are not between the two lines on the same side of the transversal.

Answer:

B. \(\angle6,\angle7\)