Question

In the given figure, AOB is a straight line. If ∠AOC + ∠BOD = 85°, then ∠COD =

Options

• 85°

• 90°

• 95°

• 100°

Answer 1

It is given that AOC is a straight line.

Also, ∠AOC, ∠BOC, and ∠COD form a linear pair.

Therefore, their sum must be supplementary.

That is

∠AOC + ∠BOD+ ∠COD= 180°  ....(1)

It is given that

\[\angle AOC + \angle BOD = 85°\]      ......(2)

On substituting the value of (2) in (1) we get,

\[\angle COD + 85^\circ = 180^\circ \]

\[ \Rightarrow \angle OD = 180^\circ - 85^\circ \]

\[ \Rightarrow \angle COD = 95^\circ \]