Question

$LM$ is a straight line and $O$ is a point on $LM$. Line $ON$ is drawn not coinciding with $OL$ or $OM$. If $\angle MON$ is three times $\angle LON$, then $\angle MON$ is equal to:

• A. ${45}^o$
• B. ${60}^o$
• C. ${105}^o$
• D. ${135}^o$

Answer 1

The correct option is D ${135}^o$

$LM$ is a straight line, $\angle MON=3\angle LON$
$\Rightarrow$ $\angle LOM={180}^o$
$\Rightarrow$ $\angle LON+3\angle LON={180}^o$
$\Rightarrow$ $4\angle LON={180}^o$
$\Rightarrow$ $\angle LON=\frac{{180}^o}{4}={45}^o$
$\therefore$ $\angle MON=3\times {45}^o={135}^o$