if two straight lines intersect each other in such a way that one of the angles formed measures 90 degree , show that each of the remaining angles measure 90 degree

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 (90°) are known as perpendicular lines.

 

In the given figure, AB is perpendicular to CD.

Considering ?AOC = 90°.

Now, ?AOC + ?AOD = 180° [Linear pair]

? 90° + ?AOD = 180°

? ?AOD = 90°

Similarly, ?AOC + ?BOC = 180° and ?BOD + ?AOD = 180° [Both making linear pair]

So, we get ?BOC = 90° and ?BOD = 90°

Hence, ?AOC = ?AOD =?BOC = ?BOD = 90°