We know that the sum of the angles of a triangle is 180°
From the figure we have,
∠AED + 120° = 180° (Linear pair)
∠AED = 180° – 120° = 60°
We know that the sum of all angles of a triangle is 180°.
Therefore, for △ADE, we have
∠ADE + ∠AED + ∠DAE = 180°
60° + ∠ADE + 30° =180°
∠ADE = 180° – 60° – 30° = 90°
From the given figure, we have
∠FDC + 90° = 180° (Linear pair)
∠FDC = 180° – 90° = 90°
Using the same steps for △CDF, we get
∠CDF + ∠DCF + ∠DFC = 180°
90° + ∠DCF + 60° = 180°
∠DCF = 180° – 60° – 90° = 30°
Again from the figure we have
∠DCF + x = 180° (Linear pair)
30° + x = 180°
x = 180° – 30° = 150°
