In the diagram shown, ABCD is a square and point F lies on BC. DEC is equilateral and EB=EF. What is the measure of EBC?
D C B A E F


Answer:

75

Step by Step Explanation:
  1. Given, ABCD is a square, DEC is an equilateral triangle and EB=EF.
    DCB=90 and DCE=60
    ECF=30
  2. Since DC=CE     [Sides of an equilateral triangle]
    and DC=CB     [Sides of a square]
    CE=CB
    ECB is an isosceles triangle.
    EBC=BEC            [Angles opposite to equal sides of a triangle are equal]    
    Now, ECB+EBC+BEC=180            [ Angle Sum Property of a triangle]
    EBC+EBC+30=180
    EBC=(18030)2=75
  3. Given, EB=EF
    BFE=EBC=75
  4. Hence, the value of EBC is 75.

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