Question

solve for x
14)
15)
16)
17)

Explanation:

14)

Step1: Use the property of supplementary angles

When two angles are supplementary, their sum is \(180^{\circ}\). So, \((x + 134)+(x + 60)=180\).

Step2: Simplify the equation

Combine like - terms: \(2x+194 = 180\).

Step3: Solve for \(x\)

Subtract \(194\) from both sides: \(2x=180 - 194=-14\). Then divide by \(2\): \(x=-7\).

15)

Step1: Use the property of alternate - exterior angles

Since the lines are parallel, \(14x + 8=15x\).

Step2: Solve for \(x\)

Subtract \(14x\) from both sides: \(x = 8\).

16)

Step1: Use the property of corresponding angles

The angle adjacent to \(100^{\circ}\) is \(180 - 100=80^{\circ}\). Then, since the lines are parallel, \(105+x = 80\).

Step2: Solve for \(x\)

Subtract \(105\) from both sides: \(x=80 - 105=-25\).

17)

Step1: Use the property of supplementary angles

\((61 + x)+(x + 141)=180\).

Step2: Simplify the equation

Combine like - terms: \(2x+202 = 180\).

Step3: Solve for \(x\)

Subtract \(202\) from both sides: \(2x=180 - 202=-22\). Then divide by \(2\): \(x=-11\).

Answer:

1. \(x=-7\)
2. \(x = 8\)
3. \(x=-25\)
4. \(x=-11\)