A right angle by two rays emanating from its vertex is divided into three angles, one of which is equal

A right angle by two rays emanating from its vertex is divided into three angles, one of which is equal to the difference between the other two angles. Find the largest of these angles?

Let the first angle formed by the ray emanating from the vertex of the right angle be x degrees, and the second angle be y degrees. Then the third angle, in accordance with the condition of this task, will be equal to (x – y) degrees.

Also, note that the largest of these three (x, y, and x – y) is x.

Therefore, you can draw up the following equality and calculate what x is equal to:

x + y + (x – y) = 90o;
x + y + x – y = 90o;
2 * x = 90o;
x = 90o: 2 = 45o.

Answer: The largest angle is 45 degrees.