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°.​

Answer 1

Step-by-step explanation:

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

∠AOC = ∠BOD = 90o

From the figure we also know that ∠AOC and ∠AOD form a linear pair So it can be written as

∠AOC + ∠AOD = 180o

Substituting the values 90o + ∠AOD = 180o

On further calculation ∠AOD = 180o – 90o

By subtraction ∠AOD = 90o

From the figure we also know that ∠BOC = ∠AOD are vertically opposite angles ∠BOC = ∠AOD = 90o

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

Answer 2

Answer:

let the straight lines be AB and BC

∠AOD = 90°(given)

∠AOD= ∠COB= 90°(vertical opposite angles)

∠COB+ ∠BOD= 180°(linear pair)

90°+∠BOD= 180°

∠BOD= 180°-90°

∠BOD= 90°

∠BOD= ∠AOC=90°(vertical opposite angles)

hope it helps you

@helping human