Question

If $AB\parallel CD$ and $\angle AMO={130}^o$ and $\angle DNO={30}^o$. Find $\angle MON$.

• A. ${85}^o$
• B. ${80}^o$
• C. ${75}^o$
• D. ${90}^o$

Answer 1

Answer: (B)

${80}^o$

Construction:
Draw $XY\parallel AB\parallel CD$
$\angle AMO=\angle MOY$ (alternate angle)
$\therefore \angle MOY={130}^o$
$\angle MOX+\angle MOY={180}^o$ (Linear pair)
$\angle MOX={180}^o-{130}^o$
$={50}^o$
$\because AB\parallel CD$
$\therefore XY\parallel CD$
$\angle DNO=\angle NOX$
$\therefore \angle NOX={30}^o$
Now, $\angle MOX+\angle NOX=\angle MON$
${50}^o+{30}^o=\angle MON$
$\angle MON={80}^o$