The problem asks to identify the relationship between each pair of angles in the given diagram, where two parallel lines are intersected by a transversal. The angle pairs are: a) $\angle 7$ and $\angle 8$, b) $\angle 2$ and $\angle 7$, c) $\angle 1$ and $\angle 6$, d) $\angle 5$ and $\angle 7$, e) $\angle 6$ and $\angle 7$.

1. Problem Description

The problem asks to identify the relationship between each pair of angles in the given diagram, where two parallel lines are intersected by a transversal. The angle pairs are: a) $\angle 7$ and $\angle 8$, b) $\angle 2$ and $\angle 7$, c) $\angle 1$ and $\angle 6$, d) $\angle 5$ and $\angle 7$, e) $\angle 6$ and $\angle 7$.

2. Solution Steps

a) $\angle 7$ and $\angle 8$: These angles are on the same side of the transversal and are adjacent. They form a linear pair, which means they are supplementary angles. Therefore, $\angle 7$ and $\angle 8$ are consecutive interior angles on the same side of the transversal which form a straight line. They are supplementary adjacent angles forming a linear pair.

b) $\angle 2$ and $\angle 7$: These angles are on opposite sides of the transversal and are outside the two parallel lines. Hence, they are alternate exterior angles.

c) $\angle 1$ and $\angle 6$: These angles are on the same side of the transversal and are in corresponding positions. They are corresponding angles.

d) $\angle 5$ and $\angle 7$: These angles are on the same side of the transversal and are between the two parallel lines. They are consecutive interior angles or same-side interior angles.

e) $\angle 6$ and $\angle 7$: These angles are on the same side of the transversal and are adjacent. They form a linear pair, which means they are supplementary angles. They are consecutive adjacent angles.

3. Final Answer

a) Linear Pair / Supplementary Adjacent Angles

b) Alternate Exterior Angles

c) Corresponding Angles

d) Consecutive Interior Angles

e) Linear Pair / Supplementary Adjacent Angles