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Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

Triangle A B C is isosceles, and the measure of angle A is 74 degrees. What must be the measure of another angle of this triangle?

(A) 32 degrees
(B) 42 degrees
(C) 53 degrees
(D) 74 degrees
(E) It cannot be determined from the information given.

答案和解析

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.