Question

Challenge for all MODs and Stars #3

Find for x​

Answer 1

Answer:

1. Calculate some known angles:

angle -ACB = 180-(10+70)-(60+20) = 20°

angle-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:

triangle DCF congruent to triangle ACB

angle CFD = angle CBA = 60+20 = 80°

angle DFB = 180-80 = 100°

angle CDF = angle CAB = 70+10 = 80°

angle ADF = 180-80 = 100°

angle BDF = 180-100-20 = 60°

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

triangle ADF congruent to triangle BFD

angle AFD = angle BDF = 60°

angle DGF = 180-60-60 = 60° = angle AGB

angle GAB = 180-60-60 = 60°

triangle DFG (with all angles 60°) is equilateral

triangle 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:

triangle ACG congruent to triangle CAE

FC-CE = FA-AG = FE = FG

FG = FD, so FE = FD

6. With two equal sides, DFE is isosceles and conclude:

angle DEF = 30+x = (180-80)/2 = 50

x = 20° is the answer

hope it helps you mate

Mark brainlist