MHB Answer to Student's Question on Right Angle Triangle

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In a right angle triangle, one angle measures 90 degrees, which is the defining characteristic of this type of triangle. The sum of all interior angles in any triangle is always 180 degrees. Therefore, with one angle at 90 degrees, the remaining two angles must sum to 90 degrees. This means each of the other angles must be greater than 0 degrees and less than 90 degrees. Consequently, no angle in a right triangle can exceed 90 degrees.
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A student ask me the question:
Why the other angles in Right angle triangle can't be more than 90 degrees?
I want to answer him correctly to the question, What Should I Say to Him?
 
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The sum of the interior angles in a triangle is $180^{\circ}$. Given that one angle is $90^{\circ}$ this leaves $90^{\circ}$ for the sum of the other two angles, which means that for either of the other angles, they must be greater than $0^{\circ}$ and less than $90^{\circ}$.
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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