Question

1

a. ∠1 and ∠8
b. ∠2 and ∠3
c. ∠5 and ∠7
d. ∠2 and ∠7
e. ∠1 and ∠3
f. ∠6 and ∠7

Explanation:

To determine the type of each angle pair, we use angle relationship definitions (vertical, adjacent, linear pair, corresponding, alternate interior/exterior, consecutive interior):

Part a: $\angle 1$ and $\angle 8$

• $\angle 1$ is above line $r$, left of line $p$; $\angle 8$ is below line $r$, right of line $q$.
• These are alternate exterior angles (lie outside the two lines cut by a transversal, on opposite sides of the transversal).

Part b: $\angle 2$ and $\angle 3$

• $\angle 2$ and $\angle 3$ share a common side (line $r$) and a common vertex, with no overlapping interior.
• These are adjacent angles (share a side and vertex, no overlap).

Part c: $\angle 5$ and $\angle 7$

• $\angle 5$ and $\angle 7$ are formed by two intersecting lines (or transversals) and are opposite each other at the intersection.
• These are vertical angles (opposite angles formed by intersecting lines, equal in measure).

Part d: $\angle 2$ and $\angle 7$

• $\angle 2$ is above line $r$, between lines $p$ and $q$; $\angle 7$ is below line $r$, between lines $p$ and $q$.
• These are alternate interior angles (lie between the two lines cut by a transversal, on opposite sides of the transversal).

Part e: $\angle 1$ and $\angle 3$

• $\angle 1$ and $\angle 3$ are on the same side of transversal $p$ (or $q$) and in corresponding positions relative to lines $p$ and $q$.
• These are corresponding angles (occupy the same relative position at each intersection of a transversal with two lines).

Part f: $\angle 6$ and $\angle 7$

• $\angle 6$ and $\angle 7$ are on the same side of transversal $p$ (or $q$) and between the two lines cut by the transversal.
• These are consecutive interior angles (lie between the two lines, on the same side of the transversal).

Final Answers (Angle Relationship Types):

a. Alternate Exterior Angles
b. Adjacent Angles
c. Vertical Angles
d. Alternate Interior Angles
e. Corresponding Angles
f. Consecutive Interior Angles

Answer:

To determine the type of each angle pair, we use angle relationship definitions (vertical, adjacent, linear pair, corresponding, alternate interior/exterior, consecutive interior):

Part a: $\angle 1$ and $\angle 8$

• $\angle 1$ is above line $r$, left of line $p$; $\angle 8$ is below line $r$, right of line $q$.
• These are alternate exterior angles (lie outside the two lines cut by a transversal, on opposite sides of the transversal).

Part b: $\angle 2$ and $\angle 3$

• $\angle 2$ and $\angle 3$ share a common side (line $r$) and a common vertex, with no overlapping interior.
• These are adjacent angles (share a side and vertex, no overlap).

Part c: $\angle 5$ and $\angle 7$

• $\angle 5$ and $\angle 7$ are formed by two intersecting lines (or transversals) and are opposite each other at the intersection.
• These are vertical angles (opposite angles formed by intersecting lines, equal in measure).

Part d: $\angle 2$ and $\angle 7$

• $\angle 2$ is above line $r$, between lines $p$ and $q$; $\angle 7$ is below line $r$, between lines $p$ and $q$.
• These are alternate interior angles (lie between the two lines cut by a transversal, on opposite sides of the transversal).

Part e: $\angle 1$ and $\angle 3$

• $\angle 1$ and $\angle 3$ are on the same side of transversal $p$ (or $q$) and in corresponding positions relative to lines $p$ and $q$.
• These are corresponding angles (occupy the same relative position at each intersection of a transversal with two lines).

Part f: $\angle 6$ and $\angle 7$

• $\angle 6$ and $\angle 7$ are on the same side of transversal $p$ (or $q$) and between the two lines cut by the transversal.
• These are consecutive interior angles (lie between the two lines, on the same side of the transversal).

Final Answers (Angle Relationship Types):

a. Alternate Exterior Angles
b. Adjacent Angles
c. Vertical Angles
d. Alternate Interior Angles
e. Corresponding Angles
f. Consecutive Interior Angles