Exercise 4.6

1. Name two pairs of vertically opposite angles in the figure.

Solution:

(i) ∠AOD∠AOE , ∠BOCBOD

(ii) ∠AOC∠AOD, BODBOE

2. Find the measure of x, y and z without actually measuring them.

Solution:

In given figure,

∠y = ° and ∠x = ∠z

We can conclude that vertically opposite angles are equal.

Therefore, y = 160°

x + 160° = ° (in linear pair)

=> x = 180° – 160°

=> x = °

Therefore ∠x = ∠z = °

3. Give some examples of vertically opposite angles in your surroundings.

Solution:

Open scissors The corner of a book

Railroad Crossing SignA slice of pizza

Road intersectionsTwo corners of a square