Angle Chasing Problem | Find the angle θ | Geometry | Ukrainian Junior Maths Olympiad

Find the angle θ | Angle Chasing Problem | Geometry | Ukrainian Junior Maths Olympiad

Join this channel to get access to perks:

MEMBERS OF THIS CHANNEL
••••••••••••••••••••••••••••••••••••••••
Mr. Gnome
Sambasivam Sathyamoorthy
ஆத்தங்கரை சண்முகம்
Εκπαιδευτήρια Καντά
AR Knowledge
堤修一
Sidnei Medeiros Vicente
Mark Ludington
Saunak Swar

[santiagoarosam]

DEF es equilatero y sus tres ángulos valen 60° 》Ángulos en D: 40/60/80 ; en F, 20/60/100 》Ángulo en A =180-40-100=40》Ángulos en B y C: (180-40)/2=70》Ángulo buscado =180-80-70=30°
Gracias y saludos.

[miguelgnievesl]

If <CFE=20° and <DFE=60° then <AFD=100° (supplementary angles), therefore <BAC=40°. Since AB=BC then <ABC=<ACB=α. Consequently <ABC+<ACB+40°=2α+40°=180°. <DBE=α=70°. Finally <BDE+α+θ=80°+70°+θ=180°. Result: θ=30°

[Bossudeboss]

Quite simple angle-chasing problem. Still nice. 👍

[SotirakisPeklivanas]

Knowing angles AFD and BDE helps to work out the DEB=30 without the algebraic thinking. But I do appreciate the mental challenge that you place in front of your viewers😊

[quigonkenny]

As AB = AC, ∆ABC is an isosceles triangle, so ∠ABC = ∠BCA = α.

As DE = EF = FD, ∆DEF is an equilateral triangle, so ∠DEF = ∠EFD = ∠FDE = 60°.

∠DFA = 180° - 60° - 20° = 100°

∠FAD = 180° - 40° - 100° = 40°

180° - 40° = 2a
α = (180°-40°)/2 = 70°

∠FEC = 180° - 20° - 70° = 90°

θ = 180° - 90° - 60° = 30°

[honestadministrator]

angle BAC = angle DAF
=angleCFD-angleADF=20° +60°-40°
= 40°
Hereby
angle ACB = (180°-40°)/2 = 70°
so theta+60°=20°+70°i.e. theta=30°

[mustafacesur]

We can find the angle in a shorter and simpler way.

[СтасМ-ъб]

Легко вычислим угол A=40°. Тогда углы B и C =70°. И тогда искомый угол равен 180-80-70=30°

[johnoehrle]

before i clicked into the video i didn't know that AB=BC, in which case the answer is indeterminate. please do better defining problems.