Q1 of 14 Page 77

If two straight lines PQ and RS intersect at O and some vertically opposite angles are formed, let’s draw them and write the names.

Vertically Opposite Angles:

Let us understand the meaning of these words.


Vertically opposite means anything which is lying on the other side. So vertically opposite angles refer to those set of angles which are opposite to each other, in other words lying face to face to each other.


Now for this question it is given that PQ and RS are two straight lines.



So, these two lines intersect at a point O in the given manner to form a cross:



Now when these two lines intersect, two pairs of vertically opposite angles are formed.


Now from the above figure,


∠POS is lying opposite to ∠ROQ



So, our first pair of vertically opposite angles are ∠POS and ∠ROQ.


Now when we again observe the figure, we notice that ∠POR and ∠SOQ are also lying opposite to each other.



So, our second pair of vertically opposite angles is ∠POR and ∠SOQ.


Additional Information:


Vertically opposite angles are always equal.


Like in above figure, ∠POS = ∠ROQ


∠POR = ∠SOQ


Now when we observe all the angles, it forms a circle. Hence the sum of all vertically opposite angles is always 360°.


In the above figure,


∠POS + ∠ROQ + ∠POR + ∠SOQ = 360°



More from this chapter

All 14 →
2

Let’s try to write the measurement of the angles from the figure given below:


∠1=35°
 ∠2=?
∠3=?
∠4=?


write.


 2

Let’s try to write the measurement of the angles from the figure given below:


∠TOS=20°
 ∠POQ=60°
 ∠POT=?
∠ROP=?
∠QOS=?


 3

Tirtha draws two straight lines PQ and XY which intersect at O. Let’s measure the vertically opposite angles by protractor.

 4

Let’s try to find out the answer to the questions give below studying the figure beside.


i. Let’s write the names of two complementary angles.


ii. Let’s write the names of two supplementary angles.


iii. Let’s write the names of two vertically opposite angles.