Question

find the value of x.
1)

x = _
2)

x = _
3)

x = _
4)

x = _
5)

x = _
6)

x = _
7)

8)

Explanation:

Step1: Use the property of supplementary angles (sum to \(180^{\circ}\))

For problem 1: \(135+\frac{x}{2}=180\)
Subtract \(135\) from both sides: \(\frac{x}{2}=180 - 135=45\)
Multiply both sides by \(2\): \(x = 90\)

Step2: For problem 2

\((x + 18)+146=180\)
Simplify: \(x+164 = 180\)
Subtract \(164\) from both sides: \(x=180 - 164 = 16\)

Step3: For problem 3

\((x - 4)+68=180\)
Simplify: \(x + 64=180\)
Subtract \(64\) from both sides: \(x=180 - 64=116\)

Step4: For problem 4

\(5x+155=180\)
Subtract \(155\) from both sides: \(5x=180 - 155 = 25\)
Divide both sides by \(5\): \(x = 5\)

Step5: For problem 5

\((6 + x)+162=180\)
Simplify: \(x+168 = 180\)
Subtract \(168\) from both sides: \(x=180 - 168=12\)

Step6: For problem 6

\(\frac{x}{3}+105=180\)
Subtract \(105\) from both sides: \(\frac{x}{3}=180 - 105 = 75\)
Multiply both sides by \(3\): \(x = 225\)

Step7: For problem 7

\(3x+87=180\)
Subtract \(87\) from both sides: \(3x=180 - 87=93\)
Divide both sides by \(3\): \(x = 31\)

Step8: For problem 8

\((x - 17)+50=180\)
Simplify: \(x+33 = 180\)
Subtract \(33\) from both sides: \(x=180 - 33 = 147\)

Answer:

1. \(x = 90\)
2. \(x = 16\)
3. \(x = 116\)
4. \(x = 5\)
5. \(x = 12\)
6. \(x = 225\)
7. \(x = 31\)
8. \(x = 147\)