Question

Find the magnitude of angles x and y in the figure given below
$\angle AOD$ and $\angle DOB$ forms a linear pair.

Answer 1

R.E.F image

We are given,

$\angle AOD$ and $\angle DOB$ from a linear pair

also

$\angle DOB$ and $\angle BOC$ forms a linear pair

So, $m\angle AOD+m\angle DOB=180\to \left(1\right)$

$m\angle DOB+m\angle BOC=180\to \left(2\right)$

Now, $m\angle DOB={180}^{\circ }-m\angle AOD$

$={180}^{\circ }-{110}^{\circ }$

$y={70}^{\circ }$

& From (2)

$m\angle BOC={180}^{\circ }-m\angle DOB$

$={180}^{\circ }-70$

$x={110}^{\circ }$