Calculate the value of x in the given figure.

Construct a line CD to meet the line AB at point E.

From the figure, in triangle BDE,

∠CDB = ∠CEB + ∠DBE    [Exterior angle property]

On substituting the values, we get;

x = ∠CEB + 45° …. (1)

Now, in the triangle AEC,

∠CEB = ∠CAB + ∠ACE   [Exterior angle property]

On substituting the values, we get;

∠CEB = 55° + 30° 

∠CEB = 85°  …..(2)

Putting eq.(2) in eq.(1);

x = 85° + 45°

x = 130° 

 

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