Question

In the adjoining figure,$ABCD$ is a rectangle whose diagonals $AC$ and $BD$ intersect at $O$. If $\angle AOB={110}^o$, find the measure of:$\angle AOD$ and $\angle BOC$.

Answer 1

Apply the concept of supplementary angles.

$\angle AOB+\angle AOD={180}^{\circ }$

${110}^{\circ }+\angle AOD={180}^{\circ }$

so $\angle AOD={70}^o$

$\angle AOD=\angle BOC$ vertically opposite angles.

Thus, $\angle BOC={70}^{\circ }$