Question

Find 4 pairs of vertically opposite angles from the given figure.

Answer 1

Hint: Vertically opposite angles are the angles opposite to each other when two lines intersect. These angles are always equal. From the diagram it is easy to understand.

Angles with green colour are called vertically opposite angles and are equal in value. Similarly, the same is applicable with angles made by black colour.

Complete step-by-step answer:
In the question, we are given a diagram with all the angles marked on it and we have to find 4 pairs of vertically opposite angles. Diagram is as shown below:

Here, taking the top left vertex having 4 angles marked on it i.e. $\angle 1,\angle 2,\angle 3,\angle 4$ . So, as we can see it is a plus sign. So, we will consider cross angles as vertically opposite angle pairs i.e. $\angle 1,\angle 4$ is the first pair and $\angle 2,\angle 3$ is the second pair of opposite angles.
Similarly, taking the top right vertex i.e. $\angle 5,\angle 6,\angle 7,\angle 8$ . So, the pair of vertically opposite angles are $\angle 5,\angle 6$ and $\angle 7,\angle 8$ . These pairs will have the same angle.
Now, consider the left bottom side which is having angles such as $\angle 9,\angle 10,\angle 11,\angle 12$ . So, here also two pairs of opposite angles are there i.e. $\angle 9,\angle 10$ and $\angle 11,\angle 12$ .
Taking the last vertex i.e. right side bottom having angles $\angle 13,\angle 14,\angle 15,\angle 16$ . So, two pairs of opposite angles are there i.e. $\angle 13,\angle 14$ and $\angle 15,\angle 16$ .
So, there are total 16 angles which when pair up for vertically opposite pairs then there are total 8 pairs to such angles i.e. $\angle 1,\angle 4$ , $\angle 2,\angle 3$ , $\angle 5,\angle 6$ , $\angle 7,\angle 8$ , $\angle 9,\angle 10$ , $\angle 11,\angle 12$ , $\angle 13,\angle 14$ , $\angle 15,\angle 16$ .
Thus, any 4 can be listed as answers.

Note: Don’t misunderstand the meaning of this term vertically opposite angle. When two lines intersect and make a plus sign then there are such angles. By seeing opposite words don’t make a pair of angles such as $\angle 4 and \angle 13,\angle 6 and \angle 11$ . These are not vertically opposite angles as they are not made by intersection of two lines. Also, do not take $\angle 1 and \angle 3,\angle 3 and \angle 4$ as a pair of vertically opposite angles because they are considered ad top and bottom angles. So, do not make silly mistakes.