Question

1. find x.
2. find x.
3. find x.
4. find x.

Explanation:

7)

Step1: Use angle - sum property

The sum of angles on a straight - line is 180°. So, \(110+(2x + 16)=180\).

Step2: Solve the equation

First, simplify the left - hand side: \(110+2x+16 = 126+2x\). Then, the equation becomes \(126 + 2x=180\). Subtract 126 from both sides: \(2x=180 - 126=54\). Divide both sides by 2: \(x = 27\).

8)

Step1: Use vertical angles property

Vertical angles are equal. So, \(6x+4 = 78\).

Step2: Solve the equation

Subtract 4 from both sides: \(6x=78 - 4 = 74\). Divide both sides by 6: \(x=\frac{74}{6}=\frac{37}{3}\approx12.33\).

9)

Step1: Use vertical angles property

Vertical angles are equal. So, \(6x=x + 12\).

Step2: Solve the equation

Subtract \(x\) from both sides: \(6x−x=x + 12−x\), which gives \(5x=12\). Divide both sides by 5: \(x=\frac{12}{5}=2.4\).

6)

Step1: Use angle - sum property in a right - triangle

The sum of angles in a right - triangle is 180°, and one angle is 90° and another is 31°. So, \((2x + 1)+31+90 = 180\).

Step2: Simplify the left - hand side

\(2x+1+31 + 90=2x+122\). The equation is \(2x+122 = 180\).

Step3: Solve for \(x\)

Subtract 122 from both sides: \(2x=180 - 122 = 58\). Divide both sides by 2: \(x = 29\).

Answer:

1. \(x = 27\)
2. \(x=\frac{37}{3}\)
3. \(x = 2.4\)
4. \(x = 29\)