Hardest Easy Geometry Problem (SOLUTION)

This geometry problem seems easy at first but if you try to solve it using basic elementary methods, you may be stuck for a while! Although it is possible to solve it that way, it can be tedious. Instead, this problem can be solved by inserting another new isosceles triangle and then finding all the same sides. The concept of inferring other angles is known as Langley’s Adventitious Angles.

In my solution, I have first solved all the other angles that I could quickly using basic geometry. I also note the isosceles triangle CBF since it has 2 angles both equaling 50°.

Secondly, I have added another triangle BCG using a new point G. Then I note the corresponding angles and isosceles triangles.

Third and lastly, I draw the triangle GFE which is also an isosceles triangle. This means that the two corresponding angles, y, are both equal to 70°. This means that x = 70 - 40 = 30°.

This puzzle was taken from the Mind Your Decisions YouTube channel and website: https://mindyourdecisions.com/blog/2016/09/04/the-hardest-easy-geometry-problem-sunday-puzzle/

Check out the puzzle (without the solution) by clicking here!

Hardest Easy Geometry Problem (SOLUTION)
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