Question

Two straight line AB and CD intersect one another at the point O. If ∠AOC + ∠COB + ∠BOD = 274°, then ∠AOD =

(i) 86°

(ii) 90°

(iii) 94°

(iv) 137°

Answer 1

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

Thus, $\angle AOD,\angle AOC,\angle COB\mathrm{and}\angle BOD$ form a complete angle, that is the sum of these four angle is.

That is,

$\angle AOD+\angle AOC+\angle COB+\angle BOD=360°$ ... (i)

It is given that

...(ii)

Subtracting (ii) from (i), we get:

Hence, the correct choice is (a).