Question

Three lines AB, CD and EF interesect each other at O. If $\angle AOE={30}^{\circ }and\angle DOB={40}^{\circ }$ (see the figure). Find $\angle COF.$

• A. ${70}^{\circ }$
• B. ${110}^{\circ }$
• C. ${55}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is B

${110}^{\circ }$

From the given figure, we have
$\angle AOE+\angle EOD+\angle DOB={180}^{\circ }[\therefore Sumofallanglesonastraightlineis{180}^{\circ }]\Rightarrow {30}^{\circ }+\angle EOD+{40}^{\circ }={180}^{\circ }\Rightarrow \angle EOD={180}^{\circ }-{70}^{\circ }\Rightarrow \angle EOD={110}^{\circ }$
Again, $\angle EOD=\angle COF\left[verticallyoppositeangles\right]\Rightarrow \angle COF={110}^{\circ }$