Question

calculate the size of letter angle in the following figure...

Answer 1

Hola mate!

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Question: Calculate all angles in variables.

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Answer

∠2 + ∠DEA = 180° (linear pair)

∠2 = 180° - 95°

∠2 = 85°

In ΔECD

∠2 + 30° + ∠D = 180° (Angle sum property of a triangle)

85° + 30° + ∠D = 180°

        115° + ∠D = 180°

                  ∠D = 180° - 115°

                  ∠D = 65° or ∠1 = 65°

AB║DE and AC is the transversal.

∴ ∠y = ∠DEA (alternate interior angles)

  ∠y = 95°

BA║DE and BD is the transversal.

∴ ∠x = ∠1 (corresponding angles)

  ∠x = 65°

Now, we have proved that,

∠x = 65°

∠y = 95°

(other angles have been found as well :D)

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Hope it Helps!

#AimBrainly