In an isosceles right triangle, two sides are of equal length, and the angles opposite those sides are also equal. By definition, an isosceles right triangle has one 90-degree angle and two other equal angles. Since the sum of all angles in a triangle must equal 180 degrees, we can calculate the measure of the base angles.
Let’s denote the measure of one base angle as ‘x’. Therefore, the equation can be set up as follows:
90 degrees (right angle) + x + x = 180 degrees
Combining like terms, we get:
90 + 2x = 180
Subtracting 90 from both sides:
2x = 90
Dividing both sides by 2:
x = 45
So, each base angle in the isosceles right triangle ABC measures 45 degrees.