Question

10. If two straight lines intersect each other in such a way that one of the
angles formed measures 90°, show that each of the remaining angles
measures 90°.

solve it guys fast​

Answer 1

Answer:

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 ∠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°