Question

In the given figure, if $\angle AOC+\angle BOC+\angle BOD={338}^{\circ }.$ find all the four angles.

Answer 1

• Given that,
  

Angle AOC+ Angle BOC+ Angle BOD=338°

• We know that
  

Sum of all angles is 360

• Angle AOC+ Angle BOC+ Angle BOD + Angle AOD = 360
  
• 338 + angle AOD = 360 ( Acc. to Question)
  
• Angle AOD = 360-338 =22
• Angle AOD = angle BOC (Because they are vertically opposite angles)
  

They are equal to 22

• And
  
• Angle BOC + angle BOD = 180 ( Because linear pair...sum of those angles will be 180)
  
• 22+angle BOD = 180
  
• Angle BOD = 180-22
  
• Angle BOD = 158
  
• Angle BOD = Angle AOC = 158 (Because vertically opposite angles are equal)
  

Angle AOC = 158

Angle BOC = 22

Angle AOD = 22

Angle BOD = 158