Question

Two lines AB and CD intersect at O. If ∠AOC + ∠COB + ∠BOD = 270°, find the measures of ∠AOC, ∠COB, ∠BOD and ∠DOA.

Answer 1

Since, lines AB and CD intersect each other at point O.

Thus,and are vertically opposite angles.

Therefore,

…… (I)

Similarly,

…... (II)

Also, we have ,,and forming a complete angle. Thus,

It is given that

Thus, we get

From (II), we get:

We know thatand form a linear pair. Therefore, these must be supplementary.

From (I), we get: