Question

If two straight lines intersect each other in such a way that one of the angles formed measure ${90}^o$, show that each of the remaining angles measures ${90}^o$.

Answer 1

Given, two straight lines intersect each other in such a way that one of the angles formed measure 90°.

We know that, lines which intersect to form a right angle are known as perpendicular lines

In the above figure , AB is perpendicular to CD

Considering $\angle AOC=90°$

Now,

$\angle AOC+\angle AOD=180°$ [Linear pair]

$90°+\angle AOD=180°$

$\angle AOD=90°$

Similarly,

$\angle AOC+\angle BOC=180°$ and $\angle BOD+\angle AOD=180°$ [Both making linear pair]

So, we get $\angle BOC=90°$ and $\angle BOD=90°$

Hence, $\angle AOC=\angle AOD=\angle BOC=\angle BOD=90°$