Question

In the given figure 1 , AB ∥ CD, the value of x is​

Answer 1

Step-by-step explanation:

Line AB || line CD and line AF is the transversal.

∠BAF = ∠DEF ------( corresponding angles )

∠BAF = 75°

∠DEF = 75°

∠DEF + ∠CEF = 180° -------( angles in linear pair )

75° + ∠ CEF = 180°

∠CEF = 180° - 75°

∠CEF = 105°

Now, in triangle EFC,

∠FEC + ∠ECF + ∠CFE = 180° -----( sum of measures of angles of a triangle is 180°)

105° + x + 30° = 180°

135° + x = 180°

x = 180° - 135°

x = 45°

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