Geometry

Geometry Level 3

Solve for angle x x .


The answer is 20.

Abdullah Mahmood by Abdullah Mahmood , 25, USA

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1 solution

Abdullah Mahmood
May 25, 2016
  1. Calculate some known angles: ACB = 180-(10+70)-(60+20) = 20° AEB = 180-70-(60+20) = 30°
  2. 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°
  3. 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

  4. CFA with two 20° angles is isosceles, so FC = FA

  5. Draw a line CG, which bisects ACB and conclude: ACG CAE FC-CE = FA-AG = FE = FG FG = FD, so FE = FD

  6. With two equal sides, DFE is isosceles and conclude: DEF = 30+x = (180-80)/2 = 50 Answer: x = 20°
1 Helpful 0 Interesting 0 Brilliant 0 Confused

This solution is in google. :P

Jun Arro Estrella - 5 years ago

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I Know that what you are saying i took from there

Abdullah Mahmood - 5 years ago

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