Question

1. identify all the linear pairs and all the vertical angles in the diagram. 1 i dont understand yet. 2 i can do it with help. 3 i can do it on my own. 4 i can teach someone. basics of geometry

Explanation:

Step1: Recall linear - pair definition

A linear pair of angles is a pair of adjacent angles whose non - common sides are opposite rays and the sum of the angles in a linear pair is 180°.

Step2: Identify linear pairs

The linear pairs in the diagram are: ($\angle1$ and $\angle2$), ($\angle2$ and $\angle3$), ($\angle3$ and $\angle4$), ($\angle4$ and $\angle5$), ($\angle5$ and $\angle6$), ($\angle6$ and $\angle1$).

Step3: Recall vertical - angle definition

Vertical angles are two non - adjacent angles formed by two intersecting lines. Vertical angles are congruent.

Step4: Identify vertical angles

The vertical angle pairs are: ($\angle1$ and $\angle4$), ($\angle2$ and $\angle5$), ($\angle3$ and $\angle6$).

Answer:

Linear pairs: $\angle1$ and $\angle2$, $\angle2$ and $\angle3$, $\angle3$ and $\angle4$, $\angle4$ and $\angle5$, $\angle5$ and $\angle6$, $\angle6$ and $\angle1$.
Vertical angles: $\angle1$ and $\angle4$, $\angle2$ and $\angle5$, $\angle3$ and $\angle6$.