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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 ABC 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 A B C is isosceles, and the measure of angle A is 74 degrees. Let the measure of angle B be b degrees, and let the measure of angle C be c degrees. The sum of the measures of the angles of a triangle is 180 degrees, so 74 plus b plus c equals 180. An isosceles triangle has two angles of equal measure, so b equals 74, or c equals 74, or b equals c does not equal 74.

If b equals 74, then 74 plus 74 plus c equals 180, so c equals 32, and the measures of the angles of the triangle are 74 degrees, 74 degrees and 32 degrees.

If c equals 74, then 74 plus b plus 74 equals 180, so b equals 32, and the measures of the angles of the triangle are 74 degrees, 32 degrees and 74 degrees.

If b equals c, then 74 plus b plus c equals 74 plus (2 times b) equals 180, so 2 times b equals 106, and b equals c equals 53. In this case, the measures of the angles of the triangle are 74 degrees, 53 degreesand 53 degrees.

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