Răspuns:
1. a) 360°; b) unghiuri in jurul unui punct; c) 360°:5=72°
2. ∡POM=360°-(∡MON+∡NPO)=360°-(110°+150°)=100°
3. a) ∡AOC; ∡COB; ∡BOD; ∡AOD
b) ∡AOC si ∡DOB; ∡AOD si ∡BOC
c) ∡BOC≡∡AOD=45°; ∡AOC≡∡BOD=180°-45°=135°
4. a) (2x-10)+(2x+30)+(3x-10)+x+(4x-10)=360°
2x-10+2x+30+3x-10+x+4x-10=360° 12x=360° ⇒ x=30° ⇒
∡1=2·30-10=50°; ∡2=2·30+30=90°; ∡3=3·30-10=80°; ∡4=30°; ∡5=4·30-10=110°
c) ∡5=110°>90° ⇒ ∡5= unghi obtuz
5. AB∩CD={O} (ca in figura de la ex. 3)
∡AOC≡∡BOD (opuse la varf) si ∡BOC≡∡AOD (op. fv)
∡AOC+∡BOC=180°
∡AOC-∡BOC=40° ⇒ ∡AOC=40° +∡BOC
∡BOC+40°++∡BOC=180° 2∡BOC=140° ⇒ ∡BOC=70° ∡AOC=110°
Explicație pas cu pas:
