Question

directions: if (lparallel m), classify the marked angle pair and give their relationship, then solve for (x). 1. (58°) (5x - 2)° 2. (16x + 22)° 134° 3. (7x - 1)° 125° 4. (9x + 2)° 133° 5. (8x - 77)° (3x + 38)° 6. (11x - 47)° (6x - 2)° 7. (13x - 21)° (5x + 75)° 8. (9x - 33)° (5x + 3)°

Explanation:

1.

Step1: Identify angle - pair relationship

Since \(l\parallel m\), the marked angles are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal. So, we set up the equation \(58 = 5x-2\).

Step2: Solve the equation for \(x\)

Add 2 to both sides of the equation: \(58 + 2=5x-2 + 2\), which simplifies to \(60 = 5x\).

Step3: Isolate \(x\)

Divide both sides by 5: \(\frac{60}{5}=\frac{5x}{5}\), so \(x = 12\).

Step1: Identify angle - pair relationship

Since \(l\parallel m\), the marked angles are alternate - exterior angles. Alternate - exterior angles are equal when two parallel lines are cut by a transversal. So, we set up the equation \(16x+22 = 134\).

Step2: Solve the equation for \(x\)

Subtract 22 from both sides: \(16x+22-22 = 134 - 22\), which gives \(16x=112\).

Step3: Isolate \(x\)

Divide both sides by 16: \(\frac{16x}{16}=\frac{112}{16}\), so \(x = 7\).

Step1: Identify angle - pair relationship

Since \(l\parallel m\), the marked angles are same - side interior angles. Same - side interior angles are supplementary (sum to \(180^{\circ}\)). So, we set up the equation \((7x - 1)+125=180\).

Step2: Simplify the left - hand side

\(7x-1 + 125=7x+124\), so the equation becomes \(7x+124 = 180\).

Step3: Solve for \(x\)

Subtract 124 from both sides: \(7x+124-124 = 180 - 124\), which gives \(7x = 56\).

Step4: Isolate \(x\)

Divide both sides by 7: \(\frac{7x}{7}=\frac{56}{7}\), so \(x = 8\).

Answer:

\(x = 12\)

2.