Question

find the value of x that makes p || q.
4.
give the choice or choices that
5.
6.

Explanation:

1. For the first - pair of angles (Problem 4):

• When \(p\parallel q\), the corresponding angles are equal. Here, \(4x=(3x + 30)\) (corresponding - angle postulate for parallel lines).
• Step 1: Set up the equation
• We have the equation \(4x=3x + 30\). The goal is to isolate \(x\) on one side of the equation.
• Subtract \(3x\) from both sides of the equation: \(4x-3x=3x + 30-3x\).
• Step 2: Simplify the equation
• On the left - hand side, \(4x-3x=x\), and on the right - hand side, \(3x + 30-3x = 30\). So, \(x = 30\).

1. For the second - pair of angles (Problem 5):

• When \(p\parallel q\), the alternate interior angles are equal. So, \(x=(3x + 24)\) (alternate - interior angles for parallel lines).
• Step 1: Set up the equation
• \(x=3x + 24\). First, we want to get all the \(x\) terms on one side. Subtract \(3x\) from both sides: \(x-3x=3x + 24-3x\).
• Step 2: Simplify the left - hand side
• \(x-3x=-2x\), and \(3x + 24-3x = 24\). So, \(-2x=24\).
• Step 3: Solve for \(x\)
• Divide both sides by \(-2\): \(x=\frac{24}{-2}=-12\).

1. For the third - pair of angles (Problem 6):

• When \(p\parallel q\), the corresponding angles are equal. So, \(5x-10=2x + 50\) (corresponding angles for parallel lines).
• Step 1: Set up the equation
• \(5x-10=2x + 50\). Subtract \(2x\) from both sides: \(5x-2x-10=2x-2x + 50\).
• Step 2: Simplify the left - hand side
• \(5x-2x=3x\), so \(3x-10 = 50\).
• Step 3: Add 10 to both sides
• \(3x-10 + 10=50 + 10\), which gives \(3x=60\).
• Step 4: Solve for \(x\)
• Divide both sides by 3: \(x=\frac{60}{3}=20\).

Answer:

1. \(x = 30\)
2. \(x=-12\)
3. \(x = 20\)