Find the value of x.

Hi student,
Please see the diagram for the problem below ,


Calculate some known angles:
  • ACB = 180-(10+70)-(60+20) = 20°
  • AEB = 180-70-(60+20) = 30° Draw a line from point D parallel to AB, labeling the intersection with BC as a new point F and conclude:
  • DCF  ACB
  • CFD = CBA = 60+20 = 80°
  • DFB = 180-80 = 100°
  • CDF = CAB = 70+10 = 80°
  • ADF = 180-80 = 100°
  • BDF = 180-100-20 = 60°
Draw a line FA labeling the intersection with DB as a new point G and conclude:
  • ADF  BFD
  • AFD = BDF = 60°
  • DGF = 180-60-60 = 60° = AGB
  • GAB = 180-60-60 = 60°
  • DFG (with all angles 60°) is equilateral
  • AGB (with all angles 60°) is equilateral CFA with two 20° angles is isosceles, so FC = FA
. Draw a line CG, which bisects ACB and conclude:
  • ACG  CAE
  • FC-CE = FA-AG = FE = FG
  • FG = FD, so FE = FD​​​​​​​ . With two equal sides, DFE is isosceles and conclude:
  • DEF = 30+x = (180-80)/2 = 50
Answer: x = 20°

Thanks & Regards , 
Harshit Tyagi 

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Angle x = 50
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