Question

13.5 vertical angles (dok 1,2) when two lines intersect, two - pairs of vertical angles are formed. vertical angles are located across from one another and are not adjacent. they share a vertex point in common. vertical angles are congruent. congruent means they have the same measure. ∠aob and ∠cod are vertical angles. ∠aoc and ∠bod are vertical angles in the diagram below, name the second angle in each pair of vertical angles. (dok 1) 1. ∠ypv __ 2. ∠qpr 3. ∠spt 4. ∠vpt 5. ∠rpt 6. ∠vps 7. ∠mln 8. ∠klh 9. ∠gln 10. ∠glm 11. ∠klm 12. ∠hlg __ use the information given to find the measure of each unknown vertical angle. (dok 2)

Explanation:

Step1: Recall vertical - angle property

Vertical angles are congruent and are opposite each other when two lines intersect.

Step2: Name vertical - angle pairs

1. $\angle YPV$ and $\angle RPS$ are vertical angles.
2. $\angle QPR$ and $\angle VPT$ are vertical angles.
3. $\angle SPT$ and $\angle QPV$ are vertical angles.
4. $\angle VPT$ and $\angle QPR$ are vertical angles.
5. $\angle RPT$ and $\angle YPS$ are vertical angles.
6. $\angle VPS$ and $\angle QPT$ are vertical angles.
7. $\angle MLN$ and $\angle KLG$ are vertical angles.
8. $\angle KLH$ and $\angle GLM$ are vertical angles.
9. $\angle GLN$ and $\angle KLH$ are vertical angles.
10. $\angle GLM$ and $\angle KLH$ are vertical angles.
11. $\angle KLM$ and $\angle GLH$ are vertical angles.
12. $\angle HLG$ and $\angle KLM$ are vertical angles.

Step3: Find measures of vertical angles

For the first set of intersecting - line diagrams:

• If one angle is $145^{\circ}$, its vertical angle has a measure of $145^{\circ}$.
• If one angle is $35^{\circ}$, its vertical angle has a measure of $35^{\circ}$.
• If one angle is $130^{\circ}$, its vertical angle has a measure of $130^{\circ}$.
• If one angle is $50^{\circ}$, its vertical angle has a measure of $50^{\circ}$.
• If one angle is $95^{\circ}$, its vertical angle has a measure of $95^{\circ}$.
• If one angle is $85^{\circ}$, its vertical angle has a measure of $85^{\circ}$.

For the second set of intersecting - line diagrams:

• If one angle is $120^{\circ}$, its vertical angle $m\angle y = 120^{\circ}$.
• If one angle is $60^{\circ}$, its vertical angle has a measure of $60^{\circ}$.
• If one angle is $47^{\circ}$, its vertical angle $m\angle w = 47^{\circ}$.
• If one angle is $133^{\circ}$, its vertical angle has a measure of $133^{\circ}$.
• If one angle is $52^{\circ}$, its vertical angle has a measure of $52^{\circ}$.
• If one angle is $128^{\circ}$, its vertical angle has a measure of $128^{\circ}$.

Answer:

1. $\angle RPS$
2. $\angle VPT$
3. $\angle QPV$
4. $\angle QPR$
5. $\angle YPS$
6. $\angle QPT$
7. $\angle KLG$
8. $\angle GLM$
9. $\angle KLH$
10. $\angle KLH$
11. $\angle GLH$
12. $\angle KLM$
13. $120^{\circ}$
14. $60^{\circ}$
15. $47^{\circ}$