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

1.	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» 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°

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»

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°