Question

In the given figure:​ (iii)If $\angle AOB=\angle BOC=\angle COD={38}^{\circ }$ . Find reflex angle $AOC$ and reflex angle$AOD$.

Answer 1

Given:


$\angle AOB=\angle BOC=\angle COD={38}^{\circ }$

To find : Reflex angle $AOC$ and reflex angle$AOD$

We know that the sum of all the angles at a point is $360\circ$.

$\therefore$ Reflex angle $AOC={360}^{\circ }-\angle AOC$

$\Rightarrow$Reflex angle $AOC={360}^{\circ }-(\angle AOB+\angle BOC)$

$\Rightarrow$Reflex angle $AOC={360}^{\circ }-({38}^{\circ }+{38}^{\circ })$

$\Rightarrow$Reflex angle $AOC={360}^{\circ }-{76}^{\circ })$

$\therefore$ Reflex angle $AOC={284}^{\circ }$

Similarly,

Reflex $\angle AOD={360}^{\circ }-\angle AOD$

$\Rightarrow$ Reflex $\angle AOD={360}^{\circ }-(\angle AOB+\angle BOC+\angle COD$

Reflex $\angle AOD={360}^{\circ }-({38}^{\circ }+{38}^{\circ }+{38}^{\circ })$

Reflex $\angle AOD={360}^{\circ }-{114}^{\circ }$

$\therefore$ Reflex $\angle AOD={246}^{\circ }$

Hence,reflex angle $AOC={246}^{\circ }$.