Question

lines l and m are parallel

Answer 1

Answer:

• m∠ABC = 15°

Step-by-step explanation:

Given

• m∠ABC = x°
• m∠BCD = 25°
• m∠CDE = 55°
• m∠DEF = 3x°

Add two more parallel lines passing through points C and D.

Consider alternate interior angles formed by the four parallel lines.

The angles between the two middle lines are equal to:

• m∠BCD - m∠ABC  = m∠CDE - m∠DEF

Substitute values and solve for x:

• 25 - x = 55 - 3x
• 3x - x = 55 - 25
• 2x = 30
• x = 15

m∠ABC = 15°