Question

Which of the following pairs of angles are Vertical angles?

• A. $\angle AOD$ and $\angle BOC$
• B. $\angle AOE$ and $\angle COD$
• C. $\angle EOB$ and $\angle FOD$
• D. $\angle AOB$ and $\angle COD$

Answer 1

Answer: (A), (C), (D)

$\angle AOB$ and $\angle COD$

$\underset{–}{\text{Vertical Angles:}}$
Vertical angles are the pairs of opposite angles made by intersecting lines.

The given image is,

Here pair of verical angles are:

• $\angle AOD\&\angle BOC$ is a pair of non-adjacent angles formed by two intersecting lines $AC\&BD$

• $\angle AOB\&\angle DOC$ is a pair of non-adjacent angles formed by two intersecting lines $AC\&BD$

• $\angle AOE\&\angle FOC$ is a pair of non-adjacent angles formed by two intersecting lines $AC\&EF$

• $\angle BOE\&\angle DOF$ is a pair of non-adjacent angles formed by two intersecting lines $EF\&BD$

(b.) $\angle AOE$ and $\angle COD$ :
$\angle AOE$ is made by the line $AC$ and the ray $OE$ while $\angle COD$ is made by two intersecting lines $AC$ and $BD$.
Hence, they are not vertical angles.