By using properties of similar triangles and trigonometric function we got that [tex]\angle ECF=37[/tex] degree.
What are similar triangles ?
Similar triangle are those triangles whose shape is same .
Here in triangle ABC and EDC
[tex]\angle A=\angle E\\\angle B= \angle D\\[/tex]
(alternate angles)
and
[tex]\angle ACB=\angle ECD[/tex]
(vertically opposite angles)
Hence by AAA rule
[tex]\triangle ABC \sim \triangle EDC[/tex]
Now by properties of similar triangles
[tex]\frac{AC}{CE} =\frac{BC}{CD}[/tex]
in [tex]\triangle AGC[/tex]
[tex]AC^2=4^2+3^2\\\\AC=5[/tex]
in [tex]\triangle BGC[/tex]
BG=7-4=3
[tex]BC^2=4^2+4^2\\\\BC=4\sqrt2[/tex]
Now
[tex]\frac{AC}{CE} =\frac{BC}{CD}[/tex]
[tex]\frac{5}{CE} =\frac{4\sqrt2}{12\sqrt2}[/tex]
[tex]CE=5\times 3[/tex]
[tex]CE=15[/tex]
in [tex]\triangle EFC[/tex]
[tex]Sin C= \frac{EF}{EC}[/tex]
Sin C = 9/ 15
Sin C= 3/5
[tex]\angle C \approx 37[/tex] degree
By using properties of similar triangles and trigonometric function we got that [tex]\angle ECF=37[/tex] degree.
To learn more about similar triangles visit : https://brainly.com/question/14285697
