Răspuns:
Explicație pas cu pas:
∡B = 2/3 ·∡A
∡C = 1/6 ·∡A
∡D = 1 1/4 ·∡B = (1·4+1)/4 ·∡B = 5/4 ·∡B = 5/4·2/3 ·∡A = 5/6 ·∡A
∡A+∡B+∡C+∡D = 360° <=>
⁶⁾∡A+ ²⁾2/3·∡A + 1/6·∡A + 5/6·∡A = ⁶⁾360° =>
6·∡A+4·∡A+1·∡A+5·∡A = 2160° =>
16·∡A = 2160° =>
∡A = 2160°:16 =>
∡A = 135°
∡B = 2/3 ·135° = 270/3 = > ∡B = 90°
∡C = ∡A/6 = 135°/6 => ∡C = 22°30'
∡D = 5/6·135° = 675°/6 => ∡D = 112°30'
