Question

classify the angle pair as corresponding, alternate interior, alternate exterior, consecutive (same - side) interior, vertical, or supplementary/linear pair angles.

1. ∠1 and ∠9
2. ∠8 and ∠13
3. ∠6 and ∠16
4. ∠4 and ∠10
5. ∠8 and ∠16
6. ∠10 and ∠13
7. ∠10 and ∠12
8. ∠16 and ∠13

find ( m angle 1 ) and ( m angle 2 ).
9.

Explanation:

Step1: Review angle pair definitions

• Corresponding angles: Angles in the same relative position.
• Alternate interior angles: Between the two lines and on opposite sides of the transversal.
• Alternate exterior angles: Outside the two lines and on opposite sides of the transversal.
• Consecutive (same - side) interior angles: Between the two lines and on the same side of the transversal.
• Vertical angles: Opposite angles formed by two intersecting lines.
• Supplementary/linear pair angles: Adjacent angles that form a straight line ($180^{\circ}$).

Step2: Classify each angle pair

1. $\angle1$ and $\angle9$: Corresponding angles (same relative position).
2. $\angle8$ and $\angle13$: Alternate interior angles (between the lines, opposite sides of transversal).
3. $\angle6$ and $\angle16$: Alternate exterior angles (outside the lines, opposite sides of transversal).
4. $\angle4$ and $\angle10$: Corresponding angles (same relative position).
5. $\angle8$ and $\angle16$: Corresponding angles (same relative position).
6. $\angle10$ and $\angle13$: Consecutive (same - side) interior angles (between the lines, same side of transversal).
7. $\angle10$ and $\angle12$: Vertical angles (opposite angles formed by intersecting lines).
8. $\angle16$ and $\angle13$: Vertical angles (opposite angles formed by intersecting lines).

Step3: Find $m\angle1$ and $m\angle2$

• The $60^{\circ}$ angle and $\angle1$ are alternate interior angles. So, $m\angle1 = 60^{\circ}$.
• $\angle1$ and $\angle2$ are supplementary (linear pair). So, $m\angle2=180 - 60=120^{\circ}$.

Answer:

1. Corresponding angles
2. Alternate interior angles
3. Alternate exterior angles
4. Corresponding angles
5. Corresponding angles
6. Consecutive (same - side) interior angles
7. Vertical angles
8. Vertical angles
9. $m\angle1 = 60^{\circ}$, $m\angle2 = 120^{\circ}$