Question

In $\Delta MNK$, if $\angle M+\angle N={126}^o$ and $\angle M+\angle K={113}^o$, then find $\angle M,\angle N$ and $\angle K$.

• A. ${59}^o$, ${67}^o$, ${54}^o$
• B. ${62}^o$, ${63}^o$, ${50}^o$
• C. ${60}^o$, ${65}^o$, ${55}^o$
• D. ${63}^o$, ${63}^o$, ${50}^o$

Answer 1

Answer: (A)

${59}^o$, ${67}^o$, ${54}^o$

In $△MNK$,
$\angle M+\angle N={126}^o$....(i)
$\angle M+\angle K={113}^o$....(ii)
Also, we know, $\angle M+\angle K+\angle N={180}^o$ (Angle sum property)
Adding (i) and (ii)
$\angle M+\angle N+\angle M+\angle K={126}^o+{113}^o$
$180+\angle M={239}^o$
$\angle M={59}^o$
Put in equation (i)
$\angle M+\angle N={126}^o$
${59}^o+\angle N={126}^o$
$\angle N={67}^o$
Put in equation (ii)
$\angle M+\angle K={113}^o$
$59+\angle K={113}^o$
$\angle K={54}^o$.