Question

Use the diagram to complete the statement.
measure of angle ECD

Answer 1

In ∆ABC

• m<C be x

`\\ \tt\longrightarrow x+53+45=180`

`\\ \tt\longrightarrow x+98=180`

`\\ \tt\longrightarrow x=180-98`

`\\ \tt\longrightarrow x=82`

Now

m<ECD and m<ACB are opposite hence equal

Answer 2

∠ECD = 82°

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°