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Open Middle Triangle Angles Problem

[size=150]Creation of this resource was inspired by this Open Middle problem created by [url=https://twitter.com/MrJohnRowe]John Rowe[/url]. [/size]
Creation of this resource was inspired by this Open Middle problem created by John Rowe.

Can you find a solution? Change the digits on the left side. As you do, you'll see what it looks like (built to scale) on the right.

Try to find another solution different from the one you found above!

Can you find a third solution (different from the other two you found above)? Go for it!

Explain any thought process(es) or observations you noticed when attempting to find solutions to this problem.