Question

Lines AB and CD intersect at point O. If $\angle AOD={50}^{\circ }$, then match the following.

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

Answer 1

Given: $\angle AOD={50}^{\circ }$
$\angle AOD+\angle BOD={180}^{\circ }\text{(linear pair)}$
$\therefore \angle BOD={180}^{\circ }-{50}^{\circ }={130}^{\circ }$

$\angle AOD=\angle BOC$ (vertically opposite angles)
$\therefore \angle BOC={50}^{\circ }$

The sum of two complementary angles is 90°.
$\therefore$ complement of $\angle AOD={40}^{\circ }$

$\text{Reflex angle of}\angle AOD=({360}^{\circ }-{50}^{\circ })={310}^{\circ }$