Please help :) ΔDEF and ΔXYZ are similar isosceles triangles. What is the measure of angle X?

Given :  ΔDEF and ΔXYZ are similar isosceles triangles  ( see attached figure)

To find : measure of ∠X

Solution:

See attached figure

in ΔDEF

∠E = 75°

DE = DF

=> ∠F = 75°

∠E + ∠F + ∠D = 180°  ( sum of angle of triangle)

=> 75° + 75° +  ∠D = 180°  

=> ∠D = 30°  

ΔDEF  ≈ ΔXYZ

=> ∠D = ∠X    = 30°

  ∠E = ∠Y   = 75°

  ∠F = ∠Z  = 75°

∠X    = 30°  

Therefore, your answer is ∠X    = 30°  

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Step-by-step explanation: