Angles at a point

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°)

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.

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)

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 + 4x + 3x + x + 2x = 360° 12x = 360° (Adding all x terms) x = 360° ÷ 12 x = 30° Therefore, the value of x is 30°

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