Answer:
The angles are corresponding
The angles are congruent
x = 12
Step-by-step explanation:
From the given figure
∵ l // m, and t intersect them (t is the transversal)
∵ The angles of measures (4x - 6)° and (3x + 6)° are on the same side of t
∵ The angle of measure (4x - 6) above line m
∵ The angle of measure (3x + 6) above line l
∴ The angles of measures (4x - 6)° and (3x + 6)° are corresponding angles
∴ The angles are corresponding
∵ Corresponding angles are equal in measures
∴ (4x - 6)° = (3x + 6)°
∴ The angles are congruent
∵ The angles are congruent
→ Equate their measures
∴ 4x - 6 = 3x + 6
→ Add 6 to both sides
∴ 4x - 6 + 6 = 3x + 6 + 6
∴ 4x = 3x + 12
→ Subtract 3x from both sides
∴ 4x - 3x = 3x - 3x + 12
∴ x = 12
