Question

Ifin triangles $PQR$ and $LMN$, $\angle P=\angle M={60}^o,PQ:ML=PR:MN$ and $\angle N={55}^o$, then $\angle Q$ is

• A. ${50}^o$
• B. ${55}^o$
• C. ${65}^o$
• D. ${75}^o$

Answer 1

The correct option is C ${65}^o$

It is clear that $\Delta$s $PQR$ and $LMN$ are similar
$\therefore \angle R=\angle N={55}^o$
Hence, $\angle Q={180}^o-(\angle P+\angle R)$
$={180}^o-({60}^o+{55}^o)={65}^o$