Question

directions: if l || m, solve for x.
5.

1. (12x - 8)° 104°
2. (5x + 7)° (8x - 71)°
3. (7x - 61)° (4x - 7)°

Explanation:

1. Problem 5:

• Since \(l\parallel m\), the corresponding - angles are equal. So, \(9x + 2=119\).
• Step 1: Isolate the term with \(x\)
• Subtract 2 from both sides of the equation \(9x + 2=119\). The rule is that if \(a + b=c\), then \(a=c - b\). So, \(9x=119 - 2\), which simplifies to \(9x = 117\).
• Step 2: Solve for \(x\)
• Divide both sides of the equation \(9x = 117\) by 9. According to the rule if \(ax = b\) (\(a

eq0\)), then \(x=\frac{b}{a}\). So, \(x=\frac{117}{9}=13\).

1. Problem 6:

• Since \(l\parallel m\), the alternate - interior angles are equal. So, \(12x-8 = 104\).
• Step 1: Isolate the term with \(x\)
• Add 8 to both sides of the equation \(12x-8 = 104\). Using the rule if \(a - b=c\), then \(a=c + b\), we get \(12x=104 + 8\), which simplifies to \(12x = 112\).
• Step 2: Solve for \(x\)
• Divide both sides of the equation \(12x = 112\) by 12. So, \(x=\frac{112}{12}=\frac{28}{3}\approx9.33\).

1. Problem 7:

• Since \(l\parallel m\), the alternate - exterior angles are equal. So, \(5x + 7=8x-71\).
• Step 1: Move the \(x\) terms to one side
• Subtract \(5x\) from both sides: \(5x + 7-5x=8x-71-5x\), which simplifies to \(7 = 3x-71\).
• Step 2: Isolate the term with \(x\)
• Add 71 to both sides: \(7 + 71=3x-71 + 71\), so \(78 = 3x\).
• Step 3: Solve for \(x\)
• Divide both sides by 3: \(x=\frac{78}{3}=26\).

1. Problem 8:

• Since \(l\parallel m\), the corresponding angles are equal. So, \(7x-61 = 4x-7\).
• Step 1: Move the \(x\) terms to one side
• Subtract \(4x\) from both sides: \(7x-61-4x=4x-7-4x\), which simplifies to \(3x-61=-7\).
• Step 2: Isolate the term with \(x\)
• Add 61 to both sides: \(3x-61 + 61=-7 + 61\), so \(3x = 54\).
• Step 3: Solve for \(x\)
• Divide both sides by 3: \(x=\frac{54}{3}=18\).

Answer:

1. \(x = 13\)
2. \(x=\frac{28}{3}\)
3. \(x = 26\)
4. \(x = 18\)