In an isosceles right triangle, by definition, two sides are of equal length, and the angle opposite these sides is the right angle, measuring 90 degrees.
The other two angles in the triangle must be equal since it is isosceles. To find the measure of these base angles, we can use the property that the sum of the angles in any triangle is always 180 degrees.
Let’s denote each of the base angles as θ. The equation for the angles of triangle ABC can be represented as follows:
θ + θ + 90° = 180°
Combining like terms, we have:
2θ + 90° = 180°
To isolate θ, we subtract 90° from both sides of the equation:
2θ = 90°
Now, dividing both sides by 2 gives us:
θ = 45°
Thus, each of the base angles in an isosceles right triangle ABC measures 45 degrees.