Question

1. identify the lines that must be parallel based on the angle measures.
2. if a||b, m∠7 = 4x + 34 and m∠5 = 8x + 10, solve for x.
3. construct a line parallel to a given line through point r.

Explanation:

Step1: Recall angle - property for parallel lines

When \(a\parallel b\), \(\angle7\) and \(\angle5\) are alternate - interior angles and are congruent. So, \(m\angle7=m\angle5\).

Step2: Set up the equation

Set \(4x + 34=8x+10\).

Step3: Solve the equation for \(x\)

Subtract \(4x\) from both sides: \(34 = 8x+10 - 4x\), which simplifies to \(34 = 4x+10\).
Then subtract 10 from both sides: \(34 - 10=4x\), so \(24 = 4x\).
Divide both sides by 4: \(x=\frac{24}{4}=6\).

Answer:

\(x = 6\)