Đáp án:
1)
a)
$ \widehat{N}=75^{\circ}\\
\widehat{M}=105^{\circ}
b)
\widehat{N}=120^{\circ}\\
\widehat{M}=60^{\circ}\\
c)
\widehat{N}=360^{\circ}\\
\widehat{M}=144^{\circ}\\$
Giải thích các bước giải:
1)Do $\widehat{M},\widehat{N}$ kề bù nhau nên $\widehat{M}+\widehat{N}=180^{\circ}$
$\Rightarrow \widehat{M}=180^{\circ}-\widehat{N}$
a)
$\widehat{M}-\widehat{N}=30^{\circ}\\
\Rightarrow 180^{\circ}-\widehat{N}-\widehat{N}=30^{\circ}\\
\Rightarrow 2\widehat{N}=180^{\circ}-30^{\circ}=150^{\circ}\\
\Rightarrow \widehat{N}=75^{\circ}\\
\Rightarrow \widehat{M}=180^{\circ}-75^{\circ}=105^{\circ}$
b)
$2\widehat{M}=\widehat{N}\\
\Rightarrow 2.\left ( 180^{\circ}-\widehat{N} \right )=\widehat{N}\\
\Rightarrow 360^{\circ}-2\widehat{N}=\widehat{N}\\
\Rightarrow 3\widehat{N}=360^{\circ}\\
\Rightarrow \widehat{N}=120^{\circ}\\
\Rightarrow \widehat{M}=180^{\circ}-120^{\circ}=60^{\circ}\\$
c)
$\widehat{M}-4.\widehat{N}=0\\
\Rightarrow 180^{\circ}-\widehat{N}-4.\widehat{N}=0\\
\Rightarrow 180^{\circ}-5\widehat{N}=0\\
\Rightarrow 5\widehat{N}=180^{\circ}\\
\Rightarrow \widehat{N}=360^{\circ}\\
\Rightarrow \widehat{M}=180^{\circ}-36^{\circ}=144^{\circ}\\$
