Răspuns:
Scuze dar nu pot sa fac desenul. Si ultimul nu stiu cum se rezolva.
*= grade
<= unghi
Explicație pas cu pas:
13.
<AOB+<BOC+<AOC= 360*
<BOC=2<AOB+72*
<AOC=3<AOB+60*
Iar acum inlocuim:
<AOB+2<AOB+72*+3<AOB+60*=360*
6<AOB=228* => <AOB=38*
<BOC=2<AOB+72*=76*+72*=148*
<AOC=3<AOB+60*=114*+60*=174*
(OM-bis. <AOB => <AOM=<MOB= <AOB:2= 19*
(ON-bis <BOC => <BON=<NOC= <BOC:2= 74*
(OP-bis. <AOC => <AOP=<OPC= <AOC:2= 87*
<MON= <MOB+<BON= 93*
<NOP= <NOC+<OPC= 161*
14.
<AOB+<BOC+<COD+<DOA= 360*
[tex]<BOC= \frac{<AOB}{2} \\<COD= \frac{7}{6} <AOB\\<DOA= \frac{4}{3} <AOB[/tex]
Iar acum inlocuim:
[tex]<AOB+\frac{<AOB}{2} +\frac{7<AOB}{6} +\frac{4<AOB}{3} =360*\\\frac{6<AOB}{6} +\frac{3<AOB}{6} +\frac{7<AOB}{6} +\frac{8<AOB}{6} =360*[/tex]
Si amplificam toate fractiile, prima cu 6, a doua cu 3 si a patra cu 2, ca sa aiba numitorul comun 6.
[tex]\frac{24<AOB}{6} =360* \\24<AOB=2160*\\<AOB= \frac{2160}{24} =90*[/tex]
<BOC= <AOB:2= 45*
[tex]<COD= \frac{7}{6} <AOB= 105*\\<DOA= \frac{4}{3} <AOB= 120*[/tex]
<MON= <MOB+BON= 67,5*
<MOB= <AOB:2= 45* si <BON= <BOC:2= 22.5*
<NOP= <NOC+<COP= 75*
<NOC= <BOC:2= 22.5*
<COP= <COD:2= 52.5*
<POQ= <POD+<DOQ= 112.5*
<POD= <COD:2= 52,5*
<DOQ= <DOA:2=60*
<QOM=<QOA+<AOM= 105*
<QOA= <DOA:2= 60*
<AOM= <AOB:2= 45*
Sper ca te-am ajutat!
