Question

AB || CD and tranversal XY meets AB and CD at M & N respectively. If $\angle AMX={50}^{\circ }$, then

• A. ${50}^{\circ }$
• B. ${130}^{\circ }$
• C. ${40}^{\circ }$
• D. ${310}^{\circ }$

Answer 1

Given: $\angle AMX={50}^{\circ }$

$\angle CNX=\angle AMX={50}^{\circ }$ (corresponding angles are equal)

$\angle XND={180}^{\circ }-\angle CNX$
$={180}^{\circ }-{50}^{\circ }={130}^{\circ }$

Complement of $\angle AMX$
$={90}^{\circ }-{50}^{\circ }={40}^{\circ }$

Reflex angle of $\angle AMX={360}^{\circ }-{50}^{\circ }={310}^{\circ }$