The image is not that good, but, consider the following figure to be true without actually constructing it,how can one person find a $fault$ in it. The blue colour represents perpendicular, The orange represents 70 $degrees$ and the green represents 50 $degrees$. Remember, you should not construct it using a compass because it is not possible to do so.
Suppose that there exists such a triangle. Then, since every inner angle of the triangle is $60^\circ$, it has to be an equilateral triangle. Then, we know that the inner point, which is the orthocenter, has to exist on the bisector of each angle , but it does not exist on either. This is a contradiction.