In an isosceles triangle, two sides are of equal length, and the angles opposite those sides are equal. In triangle TIC, you have the vertex angle I measuring 90 degrees. This means that the two base angles, which we can call angle T and angle C, must be equal because they are opposite the two equal sides.
Since the sum of all angles in a triangle must equal 180 degrees, we can set up the following equation:
Angle I + Angle T + Angle C = 180 degrees
Substituting in what we know:
90 degrees + Angle T + Angle T = 180 degrees
90 degrees + 2 * Angle T = 180 degrees
Now, we can isolate Angle T:
2 * Angle T = 180 degrees – 90 degrees
2 * Angle T = 90 degrees
Angle T = 90 degrees / 2
Angle T = 45 degrees
Therefore, the measure of angle T is 45 degrees.