Respuesta :

semsee45

Answer:

∠ECD = 82°

Step-by-step explanation:

Alternate Interior Angles Theorem : when two parallel lines are cut by a transversal, the alternate interior angles are congruent.  Alternate angles form a Z shape and are sometimes called "Z angles".

Therefore,

∠CDF = ∠GBC = 45°

∠CEF = ∠GAC = 53°

The sum of the interior angles of a triangle is 180°

⇒ ∠ECD + ∠CDF + ∠CEF = 180

⇒ ∠ECD + 45 + 53 = 180

⇒ ∠ECD = 180 - 45 - 53 = 82°

In ∆ABC

  • m<C be x

[tex]\\ \tt\longrightarrow x+53+45=180[/tex]

[tex]\\ \tt\longrightarrow x+98=180[/tex]

[tex]\\ \tt\longrightarrow x=180-98[/tex]

[tex]\\ \tt\longrightarrow x=82[/tex]

Now

m<ECD and m<ACB are opposite hence equal

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