Răspuns:
Explicație pas cu pas:
a)
3∡BOC= 2∡AOB
∡BOC/2 + ∡AOB/2 =²⁾75°
∡BOC+∡AOB= 150°
3∡AOB+2∡BOC
∡AOB= 3/2∡ BOC
²∡⁾BOC+ 3/2∡BOC= ²⁾150°
2∡BOC+ 3∡BOC= 300°
5∡BOC= 300°
∡BOC= 300:5
∡BOC= 60°
∡AOB= 2/3 ∡BOC
∡AOB= 2/3*60 °
∡AOB= 180° /2
∡AOB= 90°
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b)
∡NOD=∡ MOD-∡MON = 90-75 =15
∡COD= ∡BOC-∡ BON- ∡NOD
∡COD= 60-30 -15=60-45= 15 °
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∡NOD= ∡COD = 15° → OD- bisectoarea ∡CON
