Question

two lines intersect at a point. the vertical angles formed are supplementary. what is the measure of each of the angles? explain

Answer 1

Refer to the attached image.

Given: Lines AB and CD intersect each other at the point O.

Since, it is given that the vertically opposite angles are supplementary.

Let the pair of vertically opposite angles $\angle BOD, \angle COA$ be supplementary angles.

So, measure of  $\angle BOD, \angle COA$ is 90 degree each.

So, $m \angle BOD = 90^\circ$ and $m \angle COA = 90^\circ$.

Now, since $\angle BOC, \angle BOD$ forms linear pair, we get

$m \angle BOC + m \angle BOD= 180^\circ$

$m \angle BOC + 90^\circ= 180^\circ$

$m \angle BOC =180^\circ- 90^\circ$

$m \angle BOC = 90^\circ$

Now, as angles BOC and AOD are vertically opposite angles.

Therefore, $m \angle AOD = 90^\circ$.

Therefore, $m \angle BOD = m \angle AOD = m \angle AOC = m \angle BOC = 90^\circ$.