Question

use the information given to find the measure of each unknown vertical angle.

1. $\angle caf = $
2. $\angle abc = $
3. $\angle kcj = $
4. $\angle abg = $
5. $\angle bcj = $
6. $\angle cab = $
7. $\angle x = $
8. $\angle y = $
9. $\angle z = $
10. $\angle w = $
11. $\angle m = $
12. $\angle p = $

Explanation:

Step1: Find $\angle CAF$ (vertical angle)

Vertical angles are equal. $\angle CAF$ is vertical to $95^\circ$.
$\angle CAF = 95^\circ$

Step2: Find $\angle ABC$ (straight angle sum)

Straight angle = $180^\circ$. $\angle ABC + 130^\circ = 180^\circ$
$\angle ABC = 180^\circ - 130^\circ = 50^\circ$

Step3: Find $\angle KCJ$ (vertical angle)

Vertical angles are equal. $\angle KCJ$ is vertical to $145^\circ$.
$\angle KCJ = 145^\circ$

Step4: Find $\angle ABG$ (vertical angle)

Vertical angles are equal. $\angle ABG$ is vertical to $130^\circ$.
$\angle ABG = 130^\circ$

Step5: Find $\angle BCJ$ (vertical angle)

Vertical angles are equal. $\angle BCJ$ is vertical to $50^\circ$.
$\angle BCJ = 50^\circ$

Step6: Find $\angle CAB$ (straight angle sum)

Straight angle = $180^\circ$. $\angle CAB + 145^\circ = 180^\circ$
$\angle CAB = 180^\circ - 145^\circ = 35^\circ$

Step7: Find $\angle x$ (vertical angle)

Vertical angles are equal. $\angle x$ is vertical to $60^\circ$.
$\angle x = 60^\circ$

Step8: Find $\angle y$ (vertical angle)

Vertical angles are equal. $\angle y$ is vertical to $120^\circ$.
$\angle y = 120^\circ$

Step9: Find $\angle z$ (vertical angle)

Vertical angles are equal. $\angle z$ is vertical to $133^\circ$.
$\angle z = 133^\circ$

Step10: Find $\angle w$ (vertical angle)

Vertical angles are equal. $\angle w$ is vertical to $47^\circ$.
$\angle w = 47^\circ$

Step11: Find $\angle m$ (vertical angle)

Vertical angles are equal. $\angle m$ is vertical to $128^\circ$.
$\angle m = 128^\circ$

Step12: Find $\angle p$ (vertical angle)

Vertical angles are equal. $\angle p$ is vertical to $52^\circ$.
$\angle p = 52^\circ$

Answer:

1. $\boldsymbol{95^\circ}$
2. $\boldsymbol{50^\circ}$
3. $\boldsymbol{145^\circ}$
4. $\boldsymbol{130^\circ}$
5. $\boldsymbol{50^\circ}$
6. $\boldsymbol{35^\circ}$
7. $\boldsymbol{60^\circ}$
8. $\boldsymbol{120^\circ}$
9. $\boldsymbol{133^\circ}$
10. $\boldsymbol{47^\circ}$
11. $\boldsymbol{128^\circ}$
12. $\boldsymbol{52^\circ}$