$\widehat{a'Pc}$ đối đỉnh $\widehat{MPN}$
$→\widehat{a'Pc}=\widehat{MPN}=60^\circ$
$\widehat{a'PM},\widehat{a'Pc}$ là hai góc kề bù
$→\widehat{a'PM}+\widehat{a'Pc}=180^\circ$ hay $\widehat{a'PM}+60^\circ=180^\circ$
$↔\widehat{a'PM}=180^\circ-60^\circ=120^\circ$
mà $\widehat{a'PM}$ đối đỉnh $\widehat{cPN}$
$→\widehat{a'PM}=\widehat{cPN}=120^\circ$
$\widehat{aNM}$ đối đỉnh $\widehat{bNP}$
$→\widehat{aNM}=\widehat{bNP}=105^\circ$
$\widehat{aNb},\widehat{bNP}$ là hai góc kề bù
$→\widehat{aNb}+\widehat{bNP}=180^\circ$ hay $\widehat{aNb}+105^\circ=180^\circ$
$↔\widehat{aNb}=180^\circ-105^\circ=75^\circ$
mà $\widehat{aNb}$ đối đỉnh $\widehat{MNP}$
$→\widehat{aNb}=\widehat{MNP}=75^\circ$
$\widehat{NMP}$ đối đỉnh $\widehat{c'Mb'}$
$→\widehat{NMP}=\widehat{c'Mb'}=45^\circ$
$\widehat{cMb'},\widehat{PMb'}$ là hai góc kề bù
$→\widehat{cMb'}+\widehat{PMb'}=180^\circ$ hay $45^\circ+\widehat{PMb'}=180^\circ$
$↔\widehat{PMb'}=180^\circ-45^\circ=135^\circ$
mà $\widehat{PMb'}$ đối đỉnh $\widehat{NMc'}$
$→\widehat{PMb'}=\widehat{NMc'}=135^\circ$
Vậy $\widehat{MPa'}=\widehat{NPc}=120^\circ,\widehat{NPM}=60^\circ,\widehat{aNb}=75^\circ,\widehat{bNP}=105^\circ,\widehat{c'Mb'}=45^\circ,\widehat{PMb'}=\widehat{NMc'}=135^\circ$