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3 years ago

Lines l and m are parallel

Mathematics

1 answer:

soldi70 [24.7K]3 years ago

4 0

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°

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