Question

Two lines AB and CD intersect at O. If ∠AOC + ∠COB + ∠BOD = 270°, then ∠AOC =

(a) 70°

(b) 80°

(c) 90°

(d) 180°

Answer 1

Let us draw the following diagram showing two linesand intersecting at a point.

Thus,,, and form a complete angle, that is the sum of these four angle is .

That is,

(I)

It is given that

(II)

Subtracting (II) from (I), we get:

If one of the four angles formed by two intersecting lines is a right angle, then each of the four angles will be a right angle.
So, ∠AOC = $90°$

Hence, the correct choice is (c).