Question

In the figure, given below $\angle$COD = 150${}^{\circ }$. Choose the correct option.

• A. $\angle$AOB = 150${}^{\circ }$, $\angle$BOC = 30${}^{\circ }$
• B. $\angle$BOC = 40${}^{\circ }$, $\angle$AOB = 150${}^{\circ }$
• C. $\angle$AOB = 15${}^{\circ }$, $\angle$BOC = 30${}^{\circ }$
• D. $\angle$AOB = 40${}^{\circ }$, $\angle$BOC = 40${}^{\circ }$

Answer 1

The correct option is A

$\angle$AOB = 150${}^{\circ }$, $\angle$BOC = 30${}^{\circ }$

In the above figure, since $\angle$AOB and $\angle$COD are vertically opposite angles, they are equal, So $\angle$AOB = 150${}^{\circ }$.

Since BOD is a straight line, $\angle$BOD =180${}^{\circ }$,

We know that $\angle$DOC = 150${}^{\circ }$,

From the figure:

$\angle$BOC + $\angle$COD = $\angle$BOD

=> $\angle$BOC + 150${}^{\circ }$ = 180${}^{\circ }$

=> $\angle$BOC = 180${}^{\circ }$ - 150${}^{\circ }$ = 30${}^{\circ }$