Try solving the following puzzle before looking at the solution!

Hardest Easy Geometry Problem

Can you solve for x?

HINT: If you try to solve it using basic elementary methods, you will be stuck for a while. Try adding an extra isosceles triangle...

Source: https://mes.fm/puzzles/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/

Source: https://mes.fm/puzzles/hardest-easy-geometry-problem/solution

New Puzzle: Missing Square Puzzle

When you rearrange the pieces in this triangle, you get the missing square. Can you figure out why?

Source: https://mes.fm/puzzles/missing-square-puzzle

I will share the solution here next month!

More Puzzles

The above puzzles were taken from my website and republished on the Hive blockchain.

For more puzzles, visit: https://mes.fm/puzzles