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### 2 Answers

- PopeLv 71 month ago
I am not sure how clear this image will appear, but it should be easier to form a picture if you have it plotted to scale. All of those labeled angle measures should be easy enough to derive by walking through the triangles.

EB/ED = ABsin(5°) / [ADsin(25°)]

EB/ED = sin(80°)sin(5°) / [sin(70°)sin(25°)]

ED/EC = sin(45°)/sin(30°) = √(2)

EB/EC = (ED/EC)(EB/ED)

EB/EC = √(2)sin(80°)sin(5°) / [sin(70°)sin(25°)]

Let this ratio EB/EC be called r.

r ≈ 0.3057

EB/EC = sin(x) / sin(105° - x)

sin(x) / sin(105° - x) = r

sin(x) = rsin(105° - x)

sin(x) = rsin(105°)cos(x) - rsin(x)cos(105°)

sin(x)[1 + rcos(105°)] = rsin(105°)cos(x)

tan(x) = rsin(105°) / [1 + rcos(105°)]

x ≈ 17.78°

- Engr. RonaldLv 71 month ago
= 80 + 30 = 110°

=180 - 110 - 25 =45°

25 + 5 = 30°

180 - 80 - 30 = 70°

180 - 70 - 5 = 105°

180 - 105 = 75°

180 - 75 = 105°

180 - 105 - 30 = 45°

x + 45 + 30 = 180

x +75 = 180

x = 180 - 75

x = 105 Answer//