1. Angles at a point

2. Angles at a point In Fig. four angles are formed at the point ‘o’.
In point ‘O’ it forms a complete angle which measures 360°
So the sum of the four angles formed is 360°
(i.e., ∠A + ∠B + ∠C + ∠D = 360°)

3. Vertically opposite angles
If two straight lines AB and CD intersect at a point ‘O’.
∠AOC and ∠BOD (i.e., ∠1 and ∠2) form one pair of vertically opposite angles
∠DOA and ∠COB (i.e., ∠3 and ∠4) form another pair of vertically opposite angles.

4. Example 1: From the figure, Identify
a) Two pairs of vertically opposite angles.
Solution:
Two pairs of vertically opposite angles.
∠BOC and ∠AOD (As shown in the fig, ∠1 and ∠2 are opposite angles)
∠COA and ∠DOB (As shown in the fig, ∠3 and ∠4 are opposite angles)

5. Example 2: Find the value of x in the given figure. Solution:
From the figure , ∠BOC = 2X , ∠COA = 4x , ∠AOD= 3x , ∠DOE = x and ∠EOB = 2x
We know that the sum of all angles at a point is 360°
∠BOC ∠COA + ∠AOD + ∠DOE + ∠EOB = 360°
2x x x x x = 360°
12x = ° (Adding all x terms)
x = 360° ÷ 12
x = 30°
Therefore, the value of x is 30°

6. Try these The sum of all angles at a point is __________
2. From the figure, find
(ii) Vertically opposite angles
3. Find the value of x in the given figure