Question

1. using the diagram to the right, identify 3 linear pairs. (example: ∠hbv, ∠bvl is one pair) now, identify 3 pairs of vertical angles. (example: ∠hbv, ∠mvl is one pair)

Explanation:

Step1: Recall linear - pair definition

A linear pair is a pair of adjacent angles whose non - common sides are opposite rays.

Step2: Identify linear pairs

$\angle HBV$ and $\angle VBL$ are adjacent and their non - common sides are opposite rays. Also, $\angle MVD$ and $\angle DVP$ are a linear pair as they are adjacent and non - common sides are opposite rays. Another linear pair is $\angle CDA$ and $\angle ADP$.

Step3: Recall vertical - angles definition

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

Step4: Identify vertical angles

$\angle HBV$ and $\angle MVL$ are vertical angles. $\angle BVM$ and $\angle HVL$ are vertical angles. $\angle CDA$ and $\angle MDP$ are vertical angles.

Answer:

Three linear pairs: $\angle HBV,\angle VBL$; $\angle MVD,\angle DVP$; $\angle CDA,\angle ADP$
Three pairs of vertical angles: $\angle HBV,\angle MVL$; $\angle BVM,\angle HVL$; $\angle CDA,\angle MDP$