Question

FIND THE VALUE OF X IN THE FIGURE ! ITS HARDEST EASY LOOKING FIGURE! CANT BE DONW WITHOUT CONSTRUCTION

Answer 1

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Answer 2

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QUESTION-FIND THE VALUE OF X IN THE FIGURE ! ITS HARDEST EASY LOOKING FIGURE! CANT BE DONW WITHOUT CONSTRUCTION

ANSWER-

Calculate some known angles:

ACB = 180-(10+70)-(60+20) = 20°

AEB = 180-60-(50+30) = 40°

2. Draw a line from point E parallel to AB, labeling the intersection with AC as a new point F and conclude:

FCE  ACB

CEF = CBA = 50+30 = 80°

FEB = 180-80 = 100°

AEF = 100-40 = 60°

CFE = CAB = 60+20 = 80°

EFA = 180-80 = 100°

3. Draw a line FB labeling the intersection with AE as a new point G and conclude:

AFE  BEF

AFB = BEA = 40°

BFE = AEF = 60°

FGE = 180-60-60 = 60° = AGB.

ABG = 180-60-60 = 60°

4. Draw a line DG. Since AD=AB (leg of isosceles) and AG=AB (leg of equilateral), conclude:

AD = AG.

DAG is isosceles

ADG = AGD = (180-20)/2 = 80°

5. Since DGF = 180-80-60 = 40°, conclude:

FDG (with two 40° angles) is isosceles, so DF = DG

6. With EF = EG (legs of equilateral) and DE = DE (same line segment) conclude:

DEF  DEG by side-side-side rule

DEF = DEG = x

FEG = 60 = x+x

Answer: x = 30°