Respuesta :

fieryanswererft

Answer:

m∠4 = 140°

Step-by-step explanation:

m∠1 = m∠4  (parallel lines with same angle)

m∠2 = m∠3  (parallel lines with same angle)

if m∠2 = m∠3 are equal:

3x + 10 = 5x - 10

3x - 5x = -10 - 10

-2x = -20

x = 10°

m∠2 = m∠3 = 3x + 10 = 3(10) + 10 = 40°

m∠1 + m∠4 + 40° + 40° = 360°

2 m∠4 = 360° - 80°

2 m∠4 = 280°

m∠4 = 140°

semsee45

Answer:

m∠4 = 140°

Step-by-step explanation:

Vertical Angle Theorem: vertical angles are always congruent.

Therefore, m∠1 = m∠4  and  m∠2 = m∠3

As m∠2 = m∠3, then

⇒ 3x + 10 = 5x - 10

⇒ 20 = 2x

⇒ x = 10

So m∠2 = 3x + 10 = 3(10) + 10 = 40°

m∠2 and m∠4 form a linear pair

Therefore m∠2 + m∠4 = 180°

⇒ 40 + m∠4 = 180

⇒ m∠4 = 140°

Linear pair: a pair of adjacent angles formed when two lines intersect.  The two angles of a linear pair always sum to 180°

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