Question

find the value of x.
19)
20)
21)
22)
23)
24)

Explanation:

19)

• Step1: Use supplementary - angle property

Supplementary angles add up to 180°. So, \(120 + 2x=180\).

• Step2: Solve for \(x\)

Subtract 120 from both sides: \(2x=180 - 120\), \(2x = 60\). Then divide both sides by 2: \(x=\frac{60}{2}=30\).

20)

• Step1: Use vertical - angle property

Vertical angles are equal. So, \(x + 12=126\).

• Step2: Solve for \(x\)

Subtract 12 from both sides: \(x=126 - 12=114\).

21)

• Step1: Use vertical - angle property

Vertical angles are equal. So, \(4x+3 = 51\).

• Step2: Solve for \(x\)

Subtract 3 from both sides: \(4x=51 - 3=48\). Then divide both sides by 4: \(x=\frac{48}{4}=12\).

22)

• Step1: Use angle - addition property

The sum of the two non - overlapping angles is equal to the larger angle. So, \(3x + 1+41=90\) (assuming it's a right - angle situation, since no other information about the overall angle is given).

• Step2: Simplify the equation

\(3x+42 = 90\).

• Step3: Solve for \(x\)

Subtract 42 from both sides: \(3x=90 - 42 = 48\). Then divide both sides by 3: \(x=\frac{48}{3}=16\).

23)

• Step1: Use vertical - angle property

Vertical angles are equal. So, \(5x=70\).

• Step2: Solve for \(x\)

Divide both sides by 5: \(x=\frac{70}{5}=14\).

24)

• Step1: Use angle - addition property

The sum of the two non - overlapping angles is 90° (assuming it's a right - angle situation). So, \(3x+5x + 2=90\).

• Step2: Combine like terms

\(8x+2 = 90\).

• Step3: Solve for \(x\)

Subtract 2 from both sides: \(8x=90 - 2=88\). Then divide both sides by 8: \(x=\frac{88}{8}=11\).

Answer:

1. \(x = 30\)
2. \(x = 114\)
3. \(x = 12\)
4. \(x = 16\)
5. \(x = 14\)
6. \(x = 11\)