Question

find the value of x.

1. (3x + 16)° 110° x =
2. 85° (4x - 5)° x =
3. 136° (2x - 18)° x =
4. (6 + 7x)° 132° x =
5. (6x + 1)° 161° x =
6. (3x - 4)° 28° x =
7. (5x + 6)° 74° x =
8. 27° (5 + 2x)° x =

Explanation:

Step1: Recall linear - pair property

The sum of angles in a linear pair is 180°.

Step2: Solve for \(x\) in problem 1

Set up the equation \((3x + 16)+110 = 180\). First, simplify the left - hand side: \(3x+126 = 180\). Then subtract 126 from both sides: \(3x=180 - 126=54\). Divide both sides by 3: \(x = 18\).

Step3: Solve for \(x\) in problem 2

Set up the equation \(85+(4x - 5)=180\). Simplify the left - hand side: \(4x + 80=180\). Subtract 80 from both sides: \(4x=100\). Divide both sides by 4: \(x = 25\).

Step4: Solve for \(x\) in problem 3

Set up the equation \(136+(2x - 18)=180\). Simplify the left - hand side: \(2x+118 = 180\). Subtract 118 from both sides: \(2x = 62\). Divide both sides by 2: \(x = 31\).

Step5: Solve for \(x\) in problem 4

Set up the equation \((6 + 7x)+132=180\). Simplify the left - hand side: \(7x+138 = 180\). Subtract 138 from both sides: \(7x = 42\). Divide both sides by 7: \(x = 6\).

Step6: Solve for \(x\) in problem 5

Set up the equation \((6x + 1)+161=180\). Simplify the left - hand side: \(6x+162 = 180\). Subtract 162 from both sides: \(6x = 18\). Divide both sides by 6: \(x = 3\).

Step7: Solve for \(x\) in problem 6

Set up the equation \((3x - 4)+28=180\). Simplify the left - hand side: \(3x + 24=180\). Subtract 24 from both sides: \(3x = 156\). Divide both sides by 3: \(x = 52\).

Step8: Solve for \(x\) in problem 7

Set up the equation \((5x + 6)+74=180\). Simplify the left - hand side: \(5x+80 = 180\). Subtract 80 from both sides: \(5x = 100\). Divide both sides by 5: \(x = 20\).

Step9: Solve for \(x\) in problem 8

Set up the equation \(27+(5 + 2x)=180\). Simplify the left - hand side: \(2x+32 = 180\). Subtract 32 from both sides: \(2x = 148\). Divide both sides by 2: \(x = 74\).

Answer:

1. \(x = 18\)
2. \(x = 25\)
3. \(x = 31\)
4. \(x = 6\)
5. \(x = 3\)
6. \(x = 52\)
7. \(x = 20\)
8. \(x = 74\)