答案：E

解析：

Triangle ABC is isosceles，and the measure of angle A is 74°. Let the measure of angle B be b°，and let the measure of angle C be c°.The sum of the measures of the angles of a triangle is 180°,so 74+b+ c = 180. An isosceles triangle has two angles of equal measure, so b= 74, or c = 74，or b= c!=74.

• If b = 74，then 74 + 74 + c = 180 ,so c = 32，and the measures of the angles of the triangle are 74°，74°and 32°.
•If c = 74，then 74 + b + 74 =180 , so b =32, and the measures of the angles of the triangle are 74°，32° and 74°.
•If b = c，then 74 + b + c = 74 + 2b=180 ,so 2b=106, and b= c = 53.In this case, the measures of the angles of the triangle are 74°，53° and 53°.

Hence if the measure of angle A is 74°，the possible measures of angles B and C， respectively, are 74° and 32°； 32°and 74°; and 53°and 53°. Therefore, it is not possible to determine what must be the measure of another angle of this triangle.