SOLUTION: What are the angle sizes in a trapezoid whose sides have lengths of 6, 20, 6, and 26? THANKS SO MUCH!!

Question 148134: What are the angle sizes in a trapezoid whose sides have lengths of 6, 20, 6, and 26? THANKS SO MUCH!!
Answer by orca(409) (Show Source): You can put this solution on YOUR website!
Label the trapezoid as ABCD, with AB parallel to CD, AD = BC = 6.
Note that trapezoid is an isosceles trapezoid as AD = BC. So
< A = < B
< C = < D
From A draw line AE perpendicular to CD.
From B draw line BF perpendicular to CD.
EF = CD - AB = 6
DE = CF = 6/2 = 3
In right triangle AED, with < AED = 90 degrees, as the hypotenuse AD is twice the leg DE, so < DAE = 30 degrees.
< D = 90 - 30 = 60 degrees
< A = < DAE + 90 degrees = 30 degrees + 90 degrees = 120 degrees
< B = < A = 120 degrees
< C = < D = 60 degrees

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