Find angle x where a figure is formed by 2 isosceles triangles

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Solution 1:

60 and (20+x) are on the same arc AB:

\[\Rightarrow \frac{60}2 = 20+x\]

\[\Rightarrow x = 10\]

Solution 2:

Triangle OAB is isosceles:

\[\Rightarrow 20+20+x = 50\]

\[\Rightarrow x = 10\]

Solution 3:

Triangle ABC is isosceles and triangle ACD is equilatereal:

\[\Rightarrow 50+x = 60\]

\[\Rightarrow x = 10\]