Question

part 2 – brain dump
what do you know about any of angles in the diagram to the left.
alternate interior
∠4=∠6
∠3=∠5
alternate
∠1=∠7

Explanation:

Step1: Identify Vertical Angles

Vertical angles are equal. For example, $\angle1$ and $\angle3$ are vertical angles, so $\angle1 = \angle3$. Similarly, $\angle2$ and $\angle4$, $\angle5$ and $\angle7$, $\angle6$ and $\angle8$ are vertical angle pairs, so $\angle2=\angle4$, $\angle5 = \angle7$, $\angle6=\angle8$.

Step2: Identify Linear Pairs

Angles in a linear pair sum to $180^\circ$. For example, $\angle1$ and $\angle2$ form a linear pair, so $\angle1+\angle2 = 180^\circ$. Similarly, $\angle2+\angle3 = 180^\circ$, $\angle3+\angle4 = 180^\circ$, $\angle4+\angle1 = 180^\circ$, and the same for the other intersection (e.g., $\angle5+\angle6 = 180^\circ$, etc.).

Step3: Identify Alternate Interior Angles (if lines are parallel)

If the two non - intersecting lines are parallel, alternate interior angles are equal. For example, $\angle4$ and $\angle6$ (alternate interior angles) would be equal, and $\angle3$ and $\angle5$ would also be equal.

Step4: Identify Alternate Exterior Angles (if lines are parallel)

If the two non - intersecting lines are parallel, alternate exterior angles are equal. For example, $\angle1$ and $\angle7$ (alternate exterior angles) would be equal, and $\angle2$ and $\angle8$ would also be equal.

Answer:

• Vertical angles are equal (e.g., $\angle1=\angle3$, $\angle2 = \angle4$, $\angle5=\angle7$, $\angle6=\angle8$).
• Angles in a linear pair sum to $180^\circ$ (e.g., $\angle1+\angle2=180^\circ$).
• If the two non - intersecting lines are parallel, alternate interior angles are equal (e.g., $\angle4=\angle6$, $\angle3=\angle5$) and alternate exterior angles are equal (e.g., $\angle1=\angle7$, $\angle2=\angle8$).