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Mhanifaidn

Answer:

  • x = 71°

Step-by-step explanation:

According to diagram we have:

  • ∠ABE ≅ ∠BEF as alternate interior angles
  • m∠ABE = m∠BEC + m∠BCE exterior angle is sum of non-adjacent interior angles
  • m∠BEC = m∠BCE as opposite sides are marked as equal

From the above statements we get:

  • m∠ABE = 2m∠BEC ⇒ 142° = 2m∠BEC ⇒ m∠BEC = 71°

And

  • m∠BEF = m∠ABE
  • x + m∠BEC = m∠ABE
  • x + 71° = 142°
  • x = 71°

Answer:

x = 71

Step-by-step explanation:

BE = BC , therefore Δ BCE is isosceles with 2 base angle congruent

∠ BEC = ∠ BCE = [tex]\frac{180-38}{2}[/tex] = [tex]\frac{142}{2}[/tex] = 71°

∠ ABE and ∠ BEF are alternate angles and are congruent , so

∠ BEF = 142°

∠ BEC + ∠ FEC = ∠ BEF , that is

71° + x = 142 ( subtract 71° from both sides )

x = 71

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