Question

Two lines AB and CD intersect at a point O such that angle BOC and angle AOD=280° find all the four angles.

Answer 1

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

It is given that

∠BOC+∠AOC=280°

we know that ∠AOD=∠BOC

so it can be written as

∠AOD+∠AOD=180°

2∠AOD=280°

∠AOD= 180/2

∠AOD=∠BOC=140°

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

So it can be written as

∠AOC+∠AOD=180°

∠AOC=40°

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

∠AOC=∠BOD=40 °

Therefore ∠AOC=40°

, ∠BOC=140°

, ∠AOD=140°

, ∠BOD=40°