Name: Understanding Vertically Opposite Angles
Uploaded: 2019-07-19
Duration: 6 min 7 s
Description: Did you know that many examples of vertically opposite angles can be seen in our daily lives? A railroad crossing sign for example. So how do we define this...

Question

If two straight lines intersect each other than four angles are formed. Let's prove that the sum of measurement of the four angles is four right angles.

Accepted Answer

Let us consider two straight lines $P R$ and $S Q$ intersecting at a common point $O$ .

We know that a right angle means that the angle is equal to $90 °$ . So, four right angles mean that the angle is equal to $(4 \times 90 °) = 360 °$ .

Now when we observe the above diagram, ray $Q O$ is perpendicular to line $P R$ .

So, $∠ P O Q + ∠ Q O R = 180 °$ ……… $(i)$ [As they form linear pair that is sum of angles in a straight line is $180 °$ ]

Similarly, ray $R O$ is perpendicular to line $S Q$ .

So, $∠ S O R + ∠ S O P = 180 °$ ……… $(i i)$ [As they form linear pair that is sum of angles in a straight line is $180 °$ ]

Now let us add equations $(i)$ and $(i i)$ . So, we get

$∠ P O Q + ∠ Q O R + ∠ S O R + ∠ S O P = 180 ° + 180 °$

$\Rightarrow ∠ P O Q + ∠ Q O R + ∠ S O R + ∠ S O P = 360 °$

Hence, all the angles sum up to four right angles that is $360 °$ .

Thus, it is proved that the sum of measurement of the four angles is four right angles.

If two straight lines intersect each other than four angles are formed. Let's prove that the sum of measurement of the four angles is four right angles.

Important Questions on Concept of Vertically Opposite Angles

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