Question

Which pair of angles are supplementary in the following diagram? Are there supplementary rays?

Answer 1

The total sum of angles $={360}^o$

$\Rightarrow {360}^o={50}^o+{120}^o+{130}^o+\angle AOD$

$\therefore \angle AOD={60}^o$

None of the pairs are supplementary. For a pair of angle to be supplementary, their sum should be ${180}^o$.

Here, $\angle BOC$ and $\angle COD={120}^o+{130}^o={250}^o\ne {180}^o$

$\angle COD$ and $\angle AOD={130}^o+{60}^o={190}^o\ne {180}^o$

$\angle DOA$ and $\angle AOB={60}^o+{50}^o={110}^o\ne {180}^o$

$\angle BOA$ and $\angle BOC={50}^o+{120}^o={170}^o\ne {180}^o$