The measure of angle K in the triangle is 66°
An isosceles triangle is a type if triangle in which two of it's sides are equal and also two of it's corresponding angles are equal.
The sum of angles in a triangle is 180°. This means that angle I + angle H + angle K = 180°
Triangle HIK is an isosceles triangle
angle K = angle 1
represent angle K by x
Therefore;
x + x + 48 = 180
2x = 180 - 48
2x = 132
x = 66
Therefore the measure of angle K is 66°