Question

1. diagram with 33°, (7x + 5)°, lines a, b converse: ____ 6. diagram with (12x − 29)°, (4x + 1)°, lines a, b converse: ____

Explanation:

Problem 4

Step1: Identify angle relationship

Since lines \(a\) and \(b\) are parallel (implied by the converse of alternate interior angles), the alternate interior angles are equal. So \(7x + 5 = 33\).

Step2: Solve for \(x\)

Subtract 5 from both sides: \(7x = 33 - 5 = 28\).
Divide by 7: \(x=\frac{28}{7}=4\).

Step1: Identify angle relationship

Since lines \(a\) and \(b\) are parallel (implied by the converse of corresponding angles), the corresponding angles are equal. So \(12x - 29 = 4x + 1\).

Step2: Solve for \(x\)

Subtract \(4x\) from both sides: \(8x - 29 = 1\).
Add 29 to both sides: \(8x = 30\).
Divide by 8: \(x=\frac{30}{8}=\frac{15}{4}=3.75\).

Answer:

\(x = 4\)

Problem 6