Question

solve for x.
21)
22)
23)
24)
25)
26)
27)
28)

Explanation:

1. For problem 21:

• Explanation:
• Step 1: Set up the equation based on vertical - angle property
• Vertical angles are equal. If we assume the two given angles \(x + 57\) and \(137+x\) are vertical angles, then \(x + 57=137 + x\). Subtracting \(x\) from both sides gives \(57 = 137\), which is a contradiction. So, we assume they are supplementary angles (since they are adjacent and form a straight - line). The sum of supplementary angles is \(180^{\circ}\). So, \((x + 57)+(137 + x)=180\).
• Step 2: Simplify the left - hand side of the equation
• Combine like terms: \(2x+194 = 180\).
• Step 3: Isolate the variable \(x\)
• Subtract 194 from both sides: \(2x=180 - 194=-14\).
• Divide both sides by 2: \(x=-7\).

1. For problem 22:

• Explanation:
• Step 1: Set up the equation based on vertical - angle property
• Since vertical angles are equal, we set \(15x+5 = 16x - 2\).
• Step 2: Isolate the variable \(x\)
• Subtract \(15x\) from both sides: \(5=x - 2\).
• Add 2 to both sides: \(x = 7\).

1. For problem 23:

• Explanation:
• Step 1: Set up the equation based on corresponding - angle property (assuming parallel lines)
• If the lines are parallel, then \(x + 106\) and \(79^{\circ}\) are supplementary angles. So, \(x+106 + 79=180\).
• Step 2: Simplify the left - hand side of the equation
• \(x + 185=180\).
• Step 3: Isolate the variable \(x\)
• Subtract 185 from both sides: \(x=180 - 185=-5\).

1. For problem 24:

• Explanation:
• Step 1: Set up the equation based on corresponding - angle property (assuming parallel lines)
• If the lines are parallel, then \(7x-3\) and \(6x + 6\) are equal (corresponding angles). So, \(7x-3=6x + 6\).
• Step 2: Isolate the variable \(x\)
• Subtract \(6x\) from both sides: \(x-3 = 6\).
• Add 3 to both sides: \(x = 9\).

1. For problem 25:

• Explanation:
• Step 1: Set up the equation based on vertical - angle property
• Since vertical angles are equal, \(8x+13=10x - 5\).
• Step 2: Isolate the variable \(x\)
• Subtract \(8x\) from both sides: \(13 = 2x-5\).
• Add 5 to both sides: \(18 = 2x\).
• Divide both sides by 2: \(x = 9\).

1. For problem 26:

• Explanation:
• Step 1: Set up the equation based on corresponding - angle property (assuming parallel lines)
• If the lines are parallel, then \(11x-9\) and \(76^{\circ}\) are supplementary angles. So, \(11x-9+76 = 180\).
• Step 2: Simplify the left - hand side of the equation
• \(11x + 67=180\).
• Step 3: Isolate the variable \(x\)
• Subtract 67 from both sides: \(11x=180 - 67 = 113\).
• \(x=\frac{113}{11}\approx10.27\).

Answer:

1. \(x=-7\)
2. \(x = 7\)
3. \(x=-5\)
4. \(x = 9\)
5. \(x = 9\)
6. \(x=\frac{113}{11}\)