Question

In Fig., the points A, O and B are collinear. Ray OC ⊥ ray OD. Check whether

(i) ∠AOD and ∠BOC are complementary, (ii) ∠AOC and ∠BOC are supplementary.

Answer 1

Since points A, O and B are collinear (Given), therefore AB is a straight line. 

(i) As O is a point on the line AB, therefore ∠AOD + ∠DOC + ∠BOC = 180° 

or, ∠AOD + ∠BOC + 90° = 180° 

or, ∠AOD + ∠BOC = 90° 

So, ∠AOD and ∠BOC are complementary angles. 

(ii) Also, ∠AOC and ∠BOC are supplementary as ∠AOC + ∠BOC = 180°