Question

Name all the pairs of vertically opposite angles in the figure given to us.

Answer 1

Hint: Vertically opposite angles are the angles that are directly opposite to each other. It is very easy to figure out the vertically opposite angles in a figure. We just have to look for a X figure. The angles that face each other and are directly opposite to each other in a X shaped structure are called as vertically opposite angles.

Complete step by step answer:
In the given question, we are required to find all the pairs of vertically opposite angles in the figure given to us. So, to look for vertically opposite angles in the figure given to us, we need to look for X shaped structures as the angles directly opposite to each other in a X shaped structure are the vertically opposite angles.

So, there are three X shaped structures in the figure and six vertically opposite angles. So, the vertically opposite angles pairs in the figure are:
\[
  \left( 1 \right)\angle AOP\,and\,\angle COQ \\
  \left( 2 \right)\angle BOP\,and\,\angle DOQ \\
  \left( 3 \right)\angle DOC\,and\,\angle BOA \\
 \]
Hence, all the vertically opposite angle pairs present in the figure given to us are listed above.

Note: Vertically opposite angles have the same measure under any circumstance. The measure of vertically opposite angles is equal irrespective of the orientation of the transversal, which means that the transversal may be parallel or may not be parallel.