Question

use the information given to find the measure of each unknown vertical angle. (dok 2)
13 m∠caf =
14 m∠abc =
15 m∠kcj =
16 m∠abg =
17 m∠bcj =
18 m∠cab =
19 m∠x =
20 m∠y =
21 m∠z =
22 m∠w =
23 m∠m =
24 m∠p =

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal.

Step2: Find \(m\angle CAF\)

\(\angle CAF\) and the \(145^{\circ}\) angle are vertical angles. So \(m\angle CAF = 145^{\circ}\).

Step3: Find \(m\angle ABC\)

\(\angle ABC\) and the \(50^{\circ}\) angle are vertical angles. So \(m\angle ABC=50^{\circ}\).

Step4: Find \(m\angle KCJ\)

\(\angle KCJ\) and the \(85^{\circ}\) angle are vertical angles. So \(m\angle KCJ = 85^{\circ}\).

Step5: Find \(m\angle ABG\)

\(\angle ABG\) and the \(130^{\circ}\) angle are vertical angles. So \(m\angle ABG = 130^{\circ}\).

Step6: Find \(m\angle BCJ\)

\(\angle BCJ\) and the \(95^{\circ}\) angle are vertical angles. So \(m\angle BCJ=95^{\circ}\).

Step7: Find \(m\angle CAB\)

\(\angle CAB\) and the \(35^{\circ}\) angle are vertical angles. So \(m\angle CAB = 35^{\circ}\).

Step8: Find \(m\angle x\)

\(\angle x\) and the \(120^{\circ}\) angle are vertical angles. So \(m\angle x = 120^{\circ}\).

Step9: Find \(m\angle y\)

\(\angle y\) and the \(60^{\circ}\) angle are vertical angles. So \(m\angle y = 60^{\circ}\).

Step10: Find \(m\angle z\)

\(\angle z\) and the \(47^{\circ}\) angle are vertical angles. So \(m\angle z = 47^{\circ}\).

Step11: Find \(m\angle w\)

\(\angle w\) and the \(133^{\circ}\) angle are vertical angles. So \(m\angle w = 133^{\circ}\).

Step12: Find \(m\angle m\)

\(\angle m\) and the \(52^{\circ}\) angle are vertical angles. So \(m\angle m = 52^{\circ}\).

Step13: Find \(m\angle p\)

\(\angle p\) and the \(128^{\circ}\) angle are vertical angles. So \(m\angle p = 128^{\circ}\).

Answer:

1. \(145^{\circ}\)
2. \(50^{\circ}\)
3. \(85^{\circ}\)
4. \(130^{\circ}\)
5. \(95^{\circ}\)
6. \(35^{\circ}\)
7. \(120^{\circ}\)
8. \(60^{\circ}\)
9. \(47^{\circ}\)
10. \(133^{\circ}\)
11. \(52^{\circ}\)
12. \(128^{\circ}\)