Question

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°.

Answer 1

Consider two lines AB and CD intersecting at a point O with ∠AOC = 90^o

From the figure we know that ∠AOC and ∠BOD are vertically opposite angles

∠AOC = ∠BOD = 90^o

From the figure we also know that ∠AOC and ∠AOD form a linear pair

So it can be written as

∠AOC + ∠AOD = 180^o

Substituting the values

90^o + ∠AOD = 180^o

On further calculation

∠AOD = 180^o – 90^o

By subtraction

∠AOD = 90^o

From the figure we also know that ∠BOC = ∠AOD are vertically opposite angles

∠BOC = ∠AOD = 90^o

Therefore, it is proved that each of the remaining angle is 90^o