Question

In the figure, OB is perpendicular to OA and $\angle BOC={49}^{\circ }$. Find the value of $\angle AOD$.

• A. ${139}^{\circ }$
• B. ${149}^{\circ }$
• C. ${239}^{\circ }$
• D. ${159}^{\circ }$

Answer 1

The correct option is A ${139}^{\circ }$

OB is perpendicular to OA.
$\therefore \angle AOB={90}^{\circ }$
Or, $\angle AOC+\angle COB={90}^{\circ }$
Or, $\angle AOC+{49}^{\circ }={90}^{\circ }$
Or, $\angle AOC={90}^{\circ }-{49}^{\circ }$
$={41}^{\circ }$
Now, COD is straight line.
$\therefore \angle COA+\angle AOD={180}^{\circ }$
Or, ${41}^{\circ }+\angle AOD={180}^{\circ }$
Or, $\angle AOD={180}^{\circ }-{41}^{\circ }$
$={139}^{\circ }$