Question

Fie semidreptele (OA, (OB, (OC astfel incat B € Int <)AOC. Precizati in care dintre urmatoarele cazuri, unghiul <)AOC este alungit.
a) m(AOB) =40° si m (BOC)= 50°.
b) m(AOB)= 123°27' si m (BOC)=56°33'
c) m(AOB)=150° si 5×m (BOC) = m (AOB)
d) m(AOB) = 100° si m(BOC)=30°+2×m(AOB):5
e) 3×m(BOC)=m(AOC) si m (AOB)=60°+m(BOC).

Answer 1

unghi AOC alungit inseamna de 180°, semidreptele AO SI OC fiind in prelungire⇒

a. AOB=40, BOC=50 suma lor ≠180⇒FALS
b.AOB=123°27", BOC=56°33" suma lor =180° ADEVARAT
c.AOB=150, BOC=150/5=30 suma lor =180° ADEVARAT
d.AOB=100, BOC=30+2*100/5=30+40=70 suma lor ≠180⇒FALS
e.3BOC=AOC,
dar AOC=AOB+BOC⇒ 3BOC=AOB+BOC
2BOC=AOB
DAR AOB=60+BOC inlocuim in relatia anterioara⇒
2BOC=60+BOC
BOC=60°
DAR MAI SUS AM AVUT RELATIA
AOB=2BOC
inlocuim BOC⇒
AOB=2*60=120
suma lor aob+boc=60+120=180°ADEVARAT