Răspuns:
5*m(∡AOC)=3*m(∡BOC) => m(∡AOC)= 3*m(∡BOC)/5 si m(∡BOC)= 5*m(∡AOC)/3
∡AOD si ∡BOC op. la varf => m(∡AOD)=m(∡BOC)
∡AOC si ∡BOD op. la varf => m(∡AOC)=m(∡BOD)
∡AOD, ∡BOD, ∡BOC, ∡AOC ∡-uri in jurul unui pct
=> m(∡AOD)+m(∡BOD)+m(∡BOC)+m(∡AOC)=360°
<=> 2* ( m(∡AOC)+ m(∡BOC) )= 360°
<=> m(∡AOC) + 5*m(∡AOC)/3 = 180° |*3
<=> 8*m(∡AOC)= 540°
<=> m(∡AOC)= 67,5° =m(∡BOD)
=> m(∡BOD)= 67,5°
