The two angles, other than the right angle itself, MUST be complementary.
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The complementary angles form a right angle with the shared ray.
The sum of two complementary angles is 90 degrees. The three angles of a triangle add up to 180 degrees. Hence, if you subtract the complementary angles from 180, you have the measure of the third angle: 180 - 90 = 90 (this is the third angle) As a rule, if two angles of a triangle are complementary, the third angle is a right angle (90 deg). The three angles together form a right triangle.
A right angled triangle can only have two acute angles.
Complimentary angles
The sum of two acute angles of a right triangle must equal 90 degrees.