Question

In the given figure, lines AB, CD and EF intersect at O. Find the measure of $\angle COF$.

• A. 100°
• B. 95°
• C. 135°
• D. 105°

Answer 1

The correct option is D 105°

Given: $\angle BOD={35}^{\circ }$
$\angle AOE={40}^{\circ }$

Here, AOB is a straight line. We know that angles on a line will sum up to ${180}^{\circ }$ (linear pair axiom).
$\Rightarrow \angle AOE+\angle EOD+\angle BOD={180}^{\circ }$
$\Rightarrow {40}^{\circ }+\angle EOD+{35}^{\circ }={180}^{\circ }$
$\Rightarrow \angle EOD={180}^{\circ }-{40}^{\circ }-{35}^{\circ }$
$\Rightarrow \angle EOD={105}^{\circ }$

Now, CD bisects EF at O.
$\Rightarrow \angle COF=\angle EOD$
(Since both are vertically opposite angles)
$\Rightarrow \angle COF={105}^{\circ }$