Question

find the value of x.
1)
2)
3)
4)
5)
6)
7)
8)

Explanation:

1. First problem:

Step1: Use angle sum property

The sum of angles is \(180^{\circ}\). So, \((x - 4)+143 + 20=180\)

Step2: Simplify the equation

\(x-4+163 = 180\), then \(x+159 = 180\)

Step3: Solve for \(x\)

\(x=180 - 159\)

2. Second problem:

Step1: Use vertical - angle property

Vertical angles are equal. So, \(x + 15+111=180\) (linear - pair)

Step2: Simplify the equation

\(x+126 = 180\)

Step3: Solve for \(x\)

\(x=180 - 126\)

3. Third problem:

Step1: Use linear - pair property

\((x + 30)+95=180\)

Step2: Simplify the equation

\(x+125 = 180\)

Step3: Solve for \(x\)

\(x=180 - 125\)

4. Fourth problem:

Step1: Use angle sum property

\(67+92+(3x)=180\)

Step2: Simplify the equation

\(159+3x = 180\)

Step3: Solve for \(x\)

\(3x=180 - 159\), then \(x=\frac{21}{3}\)

5. Fifth problem:

Step1: Use vertical - angle property

\(7x = 35\)

6. Sixth problem:

Step1: Use linear - pair property

\(128+(x - 61)=180\)

Step2: Simplify the equation

\(x+67 = 180\)

Step3: Solve for \(x\)

\(x=180 - 67\)

7. Seventh problem:

Step1: Use angle sum property

\((x - 42)+167+71=360\) (full - circle \(360^{\circ}\))

Step2: Simplify the equation

\(x+196 = 360\)

Step3: Solve for \(x\)

\(x=360 - 196\)

8. Eighth problem:

Step1: Use vertical - angle property

\(x + 28=52\)

Answer:

1. \(x = 21\)
2. \(x = 54\)
3. \(x = 55\)
4. \(x = 7\)
5. \(x = 5\)
6. \(x = 113\)
7. \(x = 164\)
8. \(x = 24\)