Why the other angles in Right angle triangle can't be more than 90 degrees?
It is a basic theorem in Euclidean geometry that the measure of the angles in any triangle sum to 180 degrees ($\displaystyle \pi$ radians). Since a right angle has, by definition, a measure of 90 degrees. That means that the measures of the other two angles must sum to 90 degrees. Since an angle in a triangle cannot have measure 0, that means the other two angles in a right triangle must measure less than 90 degrees each.
(This is, as I said, in Euclidean geometry. In "spherical geometry", for example, on the surface of a sphere, say the earth, the "prime meridian" through Greenwich, England, from the north pole to the equator, the 90 degrees east longitude, from the north pole to the equator, and the equator forms a "spherical triangle" in which all three angles are right angles.)
I've tried explaining this two ways that seem to be helpful. The first (similar to the response above) is based on the sum of the angles in a triangle adding up to 180 degrees. If m<A =90 deg and m<B =90 deg then theres nothing left over for our third angle.
The other way that has helped many students is this picture I draw. With the 90 degree angles at A and B the two lines are now parallel and will never intersect.
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